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\(T(E)\), as indicated in Fig. 3a, clearly distinguishes between the conducting state (solid curve) and the insulation state (dash curve). Note that the lattice distortions in Fig. 3b are reported in terms of the _e-ph_ coupling induced bond length variation \(y_{n}=u_{n+1}-u_{n}\) between nearest neighbors. The dashed curve there for the insulating state is effectively the same as the equilibrium (\(V=0\)) lattice distortion. In contrast, the solid curve in Fig. 3 demonstrates that a charged polaron state is formed in the conducting state toward the right-side of the OSE-substructure due to the external bias-induced spatial symmetry broken.
The polaron mechanism for the observed hysteretic conduction switching behavior in Fig. 2 can now be summarized as follows. In the equilibrium state (\(V=0\)), the OSE substructure is charge neutral, with its lowest-unoccupied and highest-occupied molecular orbital (LUMO and HOMO) electronic wave functions delocalized over the entire S-region. The chemical potentials of electrodes are the same as the Fermi energy, \(\mu_{\rm L}=\mu_{\rm R}=E_{F}\), locating in between the LUMO and HOMO levels of the OSE; no current is observed and the OSE is in an insulating state. Applying a positive bias \(V>0\), which elevates
Figure 2: The hysteretic current as the function of sweeping bias potential for the model OSE in junction with Co electrodes in the parallel configuration. The linear voltage sweep rate is at 0.1 V/sec. The insert is the bias voltage-induced charge variation in the OSE substructure. The OSE-Co metal binding parameter \(\beta=0.25\). | [
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Figure 1: Energy Density variation (integrated over \(\mu\) ) with radial parameter s of the star for two central energy densities ; \(6\times 10^{14}g/cm^{3}\) (solid line) and \(1\times 10^{15}g/cm^{3}\) (dashed line) | [
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# Low temperature correlation functions in integrable models: Derivation of the large distance and time asymptotics from the form factor expansion
B. L. Altshuler\({}^{*}\), R. M. Konik\({}^{\dagger}\), and A. M. Tsvelik\({}^{\dagger}\)
\({}^{*}\) Physics Department, Princeton University, Princeton NJ 08544, USA; Physics Department, Columbia University, New York, NY 10027; NEC-Laboratories America, Inc., 4 Independence Way, Princeton, NJ 085540,USA;
\({}^{\dagger}\)Department of Physics, Brookhaven National Laboratory, Upton, NY 11973-5000, USA
(October 12, 2023)
###### Abstract
We propose an approach to the problem of low but finite temperature dynamical correlation functions in integrable one-dimensional models with a spectral gap. The approach is based on the analysis of the leading singularities of the operator matrix elements and is not model specific. We discuss only models with well defined asymptotic states. For such models the long time, large distance asymptotics of the correlation functions fall into two universality classes. These classes differ primarily by whether the behavior of the two-particle S matrix at low momenta is diagonal or corresponds to pure reflection. We discuss similarities and differences between our results and results obtained by the semi-classical method suggested by Sachdev and Young, Phys. Rev. Lett. **78**, 2220 (1997).
pacs: 71.10.Pm, 72.80.Sk
## I | [] |
|
* (31) Ahmed Jellal, hep-th/0105303; S. Ghosh, hep-th/0405177.
* (32) C. Duval, P. A. Horvathy, Phys. Lett. B479,284(2000); C. Duval, P. A. Horvathy, J. Phys. A34:10097-10108, 2001, hep-th/0106089; P. Horvathy, M. Plyushchay, JHEP 0206 (2002), 033; Mariano A. del Olmo and M. S. Plyushchay, hep-th/0508020; P. A. Horvathy, and M. S. Plyushchay, Phys. Lett. B595(2004) 547-555, hep-th/0404137; Nucl. Phys. B714:269-291, 2005, hep-th/0502040.
* (33) O. Bertolami, J. G. Rosa, C. M. L. de Aragao, P. Castorina, and D. Zappala, Phys. Rev. D72 (2005) 025010, hep-th/0505064.
* (34) Kang Li, Jianhua Wang, Chiyi Chen, Mod. Phys. Lett. A Vol. 20, No. 28(2005) 2165-2174. | [] |
|
bottom trenches. To minimize \(N\) etching of the top trench should be stopped as soon as it reaches the level of the bottom trench. To do this we developed a simple endpoint detection method: a test line with the same width as the top trench was milled simultaneously with the top trench in the area above the bottom trench, outside the SQUID, see the line - A in Fig. 1 b). When the test line was etched down to the bottom trench, secondary electron emission, monitored during FIB-milling, was reduced and etching was terminated. The contrast between etched (darker) and unetched areas within the test line is clearly seen in Fig. 1 b). This simple endpoint detection method provided an accuracy of \(\sim\) few IJJ's.
Fig. 2 shows the Current-Voltage characteristics (IVC) at \(T\simeq 16K\) for the same SQUID. The IVC was measured in the four-probe/superconducting two-probe configuration, avoiding the contact resistance. A multi-branch structure due to one-by-one switching of IJJ's from the superconducting into the resistive state is seen. Counting the number of branches we conclude that the SQUID contains \(N=6\) stacked IJJ's with the critical current \(I_{c}\simeq 15-20\mu A\) and one larger junction with \(I_{c}\simeq 25-30\mu A\), which, however, remained in the superconducting state during experiments discussed below.
In Fig. 2 we can also see tiny "ghost" sub-branches, which sometimes are also seen | [] |
|
is seen that the yield ratio of near and far angle correlation peaks is sensitive to \(\gamma/\pi^{0}\) in the sample of events. It is also seen that this method is more effective for lower \(p_{T}^{associated}\).
## References
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* [2]K. Adcox et. al., Phy. Rev. Lett 88, 022301 (2002) ,C. Adler et. al., Phy. Rev. Lett 89, 0202301 (2002), ,S. S. Adler et. al., Phy. Rev. Lett 91, 072301 (2003)
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* (35) B.Z. Kopeliovich, J. Raufeisen and A.V. Tarasov, Phys. Lett. **B440** (1998) 151.
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|
# MAGNETIC COMPOSITES: MAGNONIC EXCITATIONS vs. THREE-DIMENSIONAL STRUCTURAL PERIODICITY
M. Krawczyk1 and H. Puszkarski
Footnote 1: Corresponding author; e-mail: [email protected]
Surface Physics Division, Faculty of Physics, Adam Mickiewicz University,
ul. Umultowska 85, 61-614 Poznan, Poland
## ABSTRACT
This study deals with the spin wave spectrum in magnetic macrostructure (composed of two ferromagnetic materials) showing a 3D periodicity: spherical ferromagnetic grains disposed in the nodes of a simple cubic crystal lattice are embedded in a matrix with different ferromagnetic properties. It is shown that the _magnonic spectrum_ of this composite structure exhibits frequency regions _forbidden_ for magnon propagation, and the energy gaps are found to be sensitive to the exchange contrast between the constituent materials as well as to the magnetization contrast. The widths of the respective magnonic gaps are studied as functions of parameters characterizing the magnetic structure.
**Keywords**: magnonic crystals, spin waves, periodic composites
**PACS numbers**: 75.50.-y; 75.30.Ds; 75.40.Gb | [] |
|
**Boost Mass and the Mechanics of Accelerated Black Holes**
**Koushik Dutta, Sourya Ray and Jennie Traschen1**
Footnote 1: Surface gravity \(\kappa\) is defined by the equation \(V^{b}\nabla_{b}V_{a}=\kappa V_{a}\), where \(V^{a}\) is the generator of the horizon
Department of Physics
University of Massachusetts
Amherst, MA 01003, USA
October 12, 2023
Dedicated to Rafael Sorkin for his many contributions to our
understanding of physics.
**ABSTRACT**
In this paper we study the concept of the _boost mass_ of a spacetime and investigate how variations in the boost mass enter into the laws of black hole mechanics. We define the boost mass as the gravitational charge associated with an asymptotic boost symmetry, similiar to how the ADM mass is associated with an asymptotic time translation symmetry. In distinction to the ADM mass, the boost mass is a relevant concept when the spacetime has stress energy at infinity, and so the spacetime is not asymptotically flat. We prove a version of the first law which relates the variation in the boost mass to the change in the area of the black hole horizon, plus the change in the area of an _acceleration horizon_, which is necessarily present with the boost Killing field, as we discuss. The C-metric and Ernst metric are two known analytical solutions to Einstein-Maxwell theory describing accelerating black holes which illustrate these concepts.
## 1 | [] |
|
Generalized canonical ensemble
The above methodology can be easily extended to the canonical ensemble provided that we can characterize the space in which the typical trajectory is embedded by a number of configurations \(\mathcal{N}(\Gamma^{*})\) where \(\Gamma^{*}\) now denotes the total number of smooth configurations in the composite phase space surface appropiately weighted by the different energies that the different regions of the surface have. Following the same principle for the evolution of the number of microstates (now weighted) we have
\[\frac{d\Gamma^{*}}{dt}=\sigma^{*}\mathcal{N}(\Gamma^{*})\] (17)
where
\[\sigma^{*}=\frac{d(-F/kT)}{dt}\] (18)
is the rate of change of the natural entropic potential which in the canonical ensemble is minus the Helmholtz free energy \(F\) in \(kT\) units. This entropic potential is related to entropy by means of the Legendre transform mechanism
\[-\frac{F}{kT}=\mathcal{S}-\frac{E}{kT}\] (19)
Note that the natural entropic potential correctly accounts for the entropic contribution of the phase space cells substracting to them the energy contribution which is now a fluctuating variable. If we define \(\mathcal{F}\equiv-F/kT\) and replace Eq.(18) in Eq.(17) we obtain
\[\frac{d\mathcal{F}}{d\Gamma^{*}}=\frac{1}{\mathcal{N}(\Gamma^{*})}\qquad \Rightarrow\qquad\mathcal{F}=\int_{1}^{\Gamma^{*}_{f}}\frac{d\Gamma^{*}}{ \mathcal{N}(\Gamma^{*})}\] (20)
where we have used that for \(\Gamma^{*}_{0}=1\) the entropic potential vanishes. For an ergodic system, despite that now regions of the phase space are weighted by their differing energy, all them can be attained in the long-time limit so that | [] |
|
\(S_{WZ}\) canceling the gauge anomaly, but also a new type of WZ term \(S_{NWZ}\), which is irrelevant to the gauge symmetry but is needed to make the SC system into the fully FC one analogous to the case of the CS model [4].
## 6 Conclusion
In conclusion, we have revisited the chain structure [9] analysis for the nontrivial \(a=1\) bosonized CSM, which belongs to one-chain system with one primary and three secondary constraints. In this chain structure formalism, we have newly defined the second-class constraints as the proper orthogonalized ones, and then have successfully converted the Dirac matrix into the symplectic one. As a result, we have resolved the unsatisfactory situation of the \(a=1\) CSM in the incomplete previous work [9]. Furthermore, based on our improved BFT method preserving the chain structure in the extended phase space, we have found the desired gauge invariant quantum action.
Through further investigation, it will be interesting to apply this newly improved BFT method to non-Abelian cases [13] as well as an Abelian four-dimensional anomalous chiral gauge theory [14], which seem to be very difficult to analyze within the framework of the original BFT formalism [5].
## Acknowledgments
The work of Y.-W. Kim was supported by the Korea Research Foundation, Grant No. KRF-2002-075-C00007. The work of Ee C.-Y. was supported by KOSEF, Grant No. R01-2000-000-00022-0. The work of Y.-J. Park was supported by Center for Quantum Spacetime through KOSEF, Grant No. R11-2005-021.
## References
* [1] P. A. M. Dirac, Lectures on quantum mechanics, Belfer graduate School, Yeshiva Univ. Press, New York (1964). | [] |
|
gitized and sent to shore.
Two nitrogen lasers are used for calibration of the detector. The first one (_fiber laser_) is mounted just above the array. Its light is guided via optical fibers of equal length to each OM pair. The fiber laser provides the OMs with simultaneous light signals in order to determine the offset for each channel. The second laser (_water laser_) is arranged 20 m below the array. Its light propagates through the water. This laser serves to monitor the water quality, in addition to dedicated environmental devices located along a separate string. In the context of
Figure 1: A schematic view of _NT200_. The expansion left-hand shows 2 pairs of optical modules (“svjaska”) with the svjaska electronics module, which houses part of the readout and control electronics.
Figure 2: Left panel: the normalized amplitude distribution for channel 2 (points – experiment, histogram – atmospheric muon simulation). Right panel: the normalized time difference of channel 42 and channel 43. Histogram - experiment, dashed histogram - expectation from atmospheric muons. | [
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Princeton, 1989.
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* (34) N. Boulanger, T. Damour, L. Gualtieri and M. Henneaux, Nucl. Phys. B **597** (2001) 127 [arXiv:hep-th/0007220]. | [] |
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with thicknesses in the nm range on top of the crystals [2, 3, 6]. For the Ru-1212Gd crystals used, it turned out that the mesa technology produced too large contact resistance between the crystal surface and the contacting Au layers to be useful.
Crystals thus have been measured in a two terminal configuration, as indicated in the inset of figure 12 [97]. For the measurement single crystals of typical in-plane sizes of 50-100 \(\mu\)m and thicknesses of 15-40 \(\mu\)m have been clamped between two contact rods such that the \(c\)-axis of the crystals was perpendicular to the contacting area. Figure 12 shows the temperature dependence of the out-of-plane resistance for two crystals that have been grown in the same batch. For crystal st07 the midpoint of the resistive transition is at 51 K, with a transition width of 10 K. Crystal st02 has a slightly higher \(T_{c}\) of 54 K. Here, the transition shows a footlike
Figure 12: Out-of-plane resistance of two Ru-1212Gd single crystals, as measured in the two-terminal configuration shown in the inset.
Figure 11: Field cooled magnetization vs. temperature (a) and zero field cooled magnetization vs. applied field (b) for a Ru-1212Gd single crystal. Fields are either applied parallel (\(H\|ab\)) to the layers or perpendicular to them (\(H\|c\)). Magnetization curves in (a) are normalized to their value at the peak near 100 K. Inset in (a) shows magnetization curves on an enlarged scale. | [
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* (10) Truong T and Bazzali D 2000 Exact low-lying states of two interacting equally charged particles in a magnetic field _Phys. Lett._**A 269** 186-193
* (11) Taut M 1999 Two particles whit opposite charge in a homogeneous magnetic field: particular analytical solutions of the two-dimensional Schrodinger equation _J. Phys A: Math. Gen._**32** 5509-5515
* (12) Pursey D L, Sveshnikov N A, Shirokov A M 1998 Electric dipole in a magnetic field: Bound states without classical turning points _Theor. and Math. Phys._**117**, 1262-1273
* (13) Arfken G B and Weber H J 2001 Mathematical Methods for Physicists, Fifth Edition, Academic Press | [] |
|
CERN-PH-TH/2005-145
TTP05-12
SFB/CPP-05-36
**Electroweak corrections to top-quark pair production in quark-antiquark annihilation**
J.H. Khn\({}^{a}\), A. Scharf\({}^{a}\), and P. Uwer\({}^{b}\)
\({}^{a}\)_Institut fr Theoretische Teilchenphysik, Universitt Karlsruhe_
_76128 Karlsruhe, Germany_
\({}^{b}\)_CERN, Department of Physics, Theory Division,_
_CH-1211 Geneva 23, Switzerland_
**Abstract**
Top-quark physics plays an important role at hadron colliders such as the Tevatron at Fermilab or the LHC at CERN. Given the planned precision at these colliders, precise theoretical predictions are required. In this paper we present the complete electroweak corrections to QCD-induced top-quark pair production in quark-antiquark annihilation. In particular we provide compact analytic expressions for the differential partonic cross section, which will be useful for further theoretical investigations | [] |
|
J. Collins: _"Renormalisation"_, Cambridge Monographs in Mathematical Physics, Cambridge University Press, 1984. S. Pocorski: _"Gauge Field Theories"_, Cambridge University Press, 1987. P. Ramond: _"Field Theory: A Modern Primer"_, Addison-Wesley, 1990. M. E. Peskin and D. V. Schroeder: _"An Introduction to Quantum Field Theory"_, Addison-Wesley, 1995. J. Zinn-Justin: _"Quantum Field Theory and Critical Phenomena"_, Oxford University Press 1993.
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* [17]H. W. Hamber and R. M. Williams: _"Newtonian potential in quantum Regge gravity"_, Nucl. Phys. B435 (1995), 361-397. O. Lauscher and M. Reuter: _"Is Quantum Einstein Gravity Nonperturbatively Renormalisable?"_, Class. Quant. Grav. 19 (2002), 483-492. O. Lauscher and M. Reuter: _"Towards Nonperturbative Renormalisability of Quantum Einstein Gravity"_, Int. J. Mod. Phys. A17 (2002), | [] |
|
integral can be safely put to zero (a non-zero lower limit of integration would merely result in corrections to scaling) leading to the scaling relation
\[a(2-b)=\frac{d}{2}(1-z^{\prime})\] (10)
and
\[\hat{S}^{\prime}(A\nu^{d/2})=\int_{0}^{\infty}\mathrm{d}xx^{1-b}\hat{\phi}(x,A \nu^{d/2}).\] (11)
The linear dependence of \(S(\nu,A)\) on \(A\) arises from \(\phi\) becoming independent of \(A\) in the limit \(A\gg\nu^{-d/2}\) (see Eq.(7)). This then leads to the scaling function \(\hat{S}(y)\sim y^{1-z^{\prime}}\) in Eq.(7). This also follows from noting that \(\hat{S}^{\prime}\) approaches a constant value for large \(A\) (Eq.(9)).
We have carried out extensive simulations with hypercubic lattices of various sizes in \(d=1,2,3\). A series of simulations with fixed size and varying speciation rate was used for the determination of the normalized RSA (\(L=200\) for \(d=2\) and \(L=100\) for \(d=1,3\), \(L\) being the side of the hypercube used). Another series of simulations, varying both the speciation rate and \(L\) was carried out to determine the SAR curves. \(S(\nu,A)\) is the mean number of species in a simulation with speciation rate \(\nu\) on a hypercubic lattice of size \(A=L^{d}\). In order to carry out the collapse, we used the automated procedure described in
Figure 2: Left column: plots of the SAR for \(d=1,2,3\) with \(\nu=0.001,0.003,0.01,0.03,0.1\). Right column: plots of the data collapse yielding a measure of the exponent \(z^{\prime}\) in Table 1. | [
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|
[18]. However, the unitarity problem of the theory is not yet settled [19].
The paper is organized as follows : in sec. II, we present the gravitational action and field equations, Cosmological solutions are given in sec. III and a brief discussions in sec. IV.
**II. GRAVITATIONAL ACTION AND FIELD EQUATIONS :**
We consider a gravitational action with higher order terms in the scalar curvature \((R)\) with a variable cosmological constant \(\left(\Lambda(t)\right)\) and variable gravitational constant \(\left(G(t)\right)\) which is given by
\[{\large I}=-\int\left[\frac{f(R)}{16\pi G(t)}+L_{m}\right]\sqrt{-g}\;d^{4}x\] (1)
where \(f(R)\) is a function of \(R\) and its higher power including cosmological constant and \({L_{m}}\) represents the matter lagrangian.
Variation of action (1) with respect to \(g_{\mu\nu}\) yields
\[f^{\prime}(R)\;R_{\mu\nu}-\frac{1}{2}\;f(R)\;g_{\mu\nu}+f^{\prime\prime}(R) \left(\nabla_{\mu}\nabla_{\nu}R-\Box{R}g_{\mu\nu}\right)+\]
\[f^{\prime\prime\prime}(R)\left(\nabla_{\mu}R\nabla_{\nu}R-\nabla^{\sigma}R \nabla_{\sigma}R\;g_{\mu\nu}\right)=-\;8\pi G\;T_{\mu\nu}\] (2)
where \(\Box=g_{\mu\nu}\nabla^{\mu}\nabla^{\nu}\) and \(\nabla_{\mu}\) is the covariant differential operator, and prime represents the derivative with respect to \(R\), \(T_{\mu\nu}\) is the energy momentum tensor for matter determined by \({L_{m}}\) .
We consider flat Robertson-Walker spacetime given by the metric
\[ds^{2}=-dt^{2}+a^{2}(t)\left[dr^{2}+r^{2}(d{\theta}^{2}+sin^{2}{\theta}d{\phi} ^{2})\right]\] (3)
where \(a(t)\) is the scale factor of the universe . The scalar curvature in this case is
\[R=-6\;[\dot{H}+2H^{2}]\] | [] |
|
sults are found for the pair-distribution function, where \(g(r)\) at smaller cutoffs has little short distance structure and lies fairly close to the Fermi gas (i.e., Hartree-Fock wave functions) values, where the correlations arise solely from Fermi statistics.
It is interesting to note that the correlations induced by the three-body force are significantly stronger at larger cutoffs. At \(\Lambda=3.0\,\mbox{fm}^{-1}\), which is the largest c | [
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Waves._ PhD Thesis, Delft University of Technology, (1997).
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|
Whereas the computation of the dark matter relic density is quite reliable (as in the version 1.3 of MicrOMEGAs), the result for the branching ratio BR\((b\to s\gamma)\) has still to be interpreted with care, notably for larger (\(\raise 1.29167pt\hbox{$>$\kern-7.5pt\raise-4.73611pt\hbox{$\sim$}}\ 5\)) values of \(\tan\beta\).
It is clear that further improvements of NMHDECAY would be desirable: more higher order corrections to both the Higgs masses and decay widths would be welcome, with the aim to reach the present accuracy in the MSSM. (Tests of NMHDECAY in the MSSM limit \(\lambda,\kappa\to 0\) with \(\mu_{\mathrm{eff}}\) fixed indicate, however, that the deviation of the mass of the lightest CP even Higgs boson w.r.t. corresponding MSSM calculations, for the same CP odd Higgs pole mass and sparticle spectra, is limited to about 3% and mostly much smaller.)
Informations on low energy precision observables are included only in the form of a rough calculation of BR\((b\to s\gamma)\), which should certainly be improved. Also the anomalous magnetic moment of the muon as well as \(\Delta\rho\) should be computed.
We plan to treat these issues in the near future.
Finally, it would be useful to be able to choose (universal) soft susy breaking terms at a GUT scale as in a mSUGRA version of the NMSSM. A corresponding code NMSPEC is in preparation.
## Acknowledgments
We thank P. Skands for comments on new SLHA and PDG particle codes, S. Kraml for helpful contributions to the squark, slepton and gluino sector, G. Belanger and A. Pukhov for help with the link to MicrOMEGAs, and M. Schumacher, S. Hesselbach and W. Porod for comments on the previous version of NMHDECAY. | [] |
|
simple energetics: high-fields stabilize the high magnetization phase and suppress the low magnetization phase. Because of this difference, polycrystalline average curves estimated for these high field measurements are no longer smooth and featureless as those for low fields, so the transition in magnetization should also become quite evident in powders and sintered samples measured at high enough fields.
The main graph in figure 5b shows a tentative phase diagram for how \(T_{SR}\) evolves with field in both orientations. Measurements made at low fields showed that \(T_{SR}\) in both directions essentially coincide at 63.3 K for this sample. However, earlier batches showed quite different values of \(T_{SR}\) (as low as 44 K) and multiple transitions, pointing to the relevance of disorder and thermal history in this system, which will be discussed later.
Figure 5: Low-temperature magnetic behaviour of YbFe\({}_{6}\)Ge\({}_{6}\). (a) Anisotropic susceptibility at \(B=0.1\) T, showing the anomalous transition around 63 K. The dotted line is the polycrystalline average. (b) Field dependence of the transition temperature \(T_{SR}\) for both orientations. The dotted lines are guides to the eyes. The left and right insets show how the transitions evolve under applied fields of 1, 2, 3, 4, and 5 T, for B\(\parallel\)a and B\(\parallel\)c respectively. | [
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* | [] |
|
In the case of a flow which is suspended from an algebraic diffeomorphism, C. Deninger and the author have proved this conjecture [8].
**Theorem 4.2**: _(C. Deninger-AD) The Guillemin-Patterson conjecture is true for flows suspended from algebraic Anosov diffeomorphisms. More specifically, if \(f:M\to M\) is an algebraic Anosov diffeomorphism with stable bundle \({\cal F}_{s}\), then the reduced cohomology \(\bar{H}^{\bullet}({\cal F}_{s})\) is finite dimensional and_
p=0rankFs(-1)ptr(f*|H-p(Fs))=x=f(x)det(1-f*|Ts,x)|det(1-f*|TxM)|.
For the proof one shows that the foliation cohomology is canonically isomorphic to Lie algebra cohomology with trivial coefficients. This is shown inductively using the Hochschild-Serre spectral sequence interatedly.
## 5 The Selberg zeta function
The Selberg zeta function for a compact Riemannian surface \(Y\) of genus \(g\geq 2\) is defined by
\[Z_{Y}(s)\ \begin{array}[]{c}{}_{\rm def}\\ {}^{=}\end{array}\ \prod_{c_{0}}\prod_{N\geq 0}\left(1-e^{-(s+N)l (c_{0})}\right),\]
where the first product runs over all primitive closed geodesics in \(Y\) which is equipped with the hyperbolic metric. Selberg showed in [18] that \(Z_{Y}\) extends to an entire function which satisfies a generalized Riemann hypothesis insofar as all zeros are in \({\mathbb{R}}\cup(\frac{1}{2}i{\mathbb{R}})\).
In [2] P. Cartier and A. Voros gave the following determinant expression.
**Theorem 5.1**: _(Cartier-Voros) We have_
\[Z_{Y}(\frac{1}{2}+s)\ =\ \left(e^{s^{2}}{\rm det}\left((\Delta_{d}+\frac{1}{4} )^{\frac{1}{2}}+s\right)\right)^{2g-2}\,{\rm det}\left((\Delta-\frac{1}{4})+s^ {2}\right).\]
_Here \(\Delta\) is the Laplace operator on functions of \(Y\) and \(\Delta_{d}\) is the Laplace operator on the sphere \(S^{2}\)._ | [] |
|
\(A\) are exactly degenerate, \(\sigma_{A}=2\sigma_{\tau}\), and the toy experiment can achieve \(~{}6\%\) fractional uncertainty on \(A\).
## 7 Prospects for the future
WMAP's on-going measurements of CMB polarization are expected to continue until at least 2006. In 2007 Planck will be launched and will start making full-sky observations of the polarization of the CMB. Planck is expected to achieve near-cosmic variance limit on \(\tau\). NASA's Beyond Einstein initiative features a CMB polarimeter called the Inflation Probe[29]. This instrument is designed to detect the signature of inflationary gravitational waves over a wide range of inflationary energy scales. This experiment will achieve cosmic variance limited precision on \(\tau\), which is essentially the same as Planck's sensitivity [30]. The European Space Agency plans a large angular scale polarimeter deployed on the International Space Station called SPORT, which
Figure 9: Individual and joint likelihood functions for the toy experiment discussed in the text, with \(f_{sky}=2.4\%\). The uncertainties from the marginalized likelihoods are \(\tau=0.12\pm 0.038\) and \(A=0.81\pm 0.15\), given a prior that \(\tau>0.04\). The joint confidence intervals correspond to \(1/\sqrt{e}\) (inner) and \(1/e\) (outer) of the maximum likelihood. This experiment can determine the redshift of the onset of reionization with a precision of \(\delta z\leq 3\) if reionization occurred at \(z>10\). | [
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_GRworkbench_ with a functional interface like that of the minimisation algorithm (3.1.1) with \(n=1\).
## 4 Conclusion
By 'gluing' together the methods described in this article, using their functional implementations, it is easy to define potentially complex numerical experiments. Figure 2 shows the interferometer described in SS3 simulated in _GRworkbench_. Physical properties of these interferometer simulations, such as the travel time of photons as measured by the elapsed proper time along the world-line of the beam-splitter, yielded important results in our recent analysis.[2] As physical situations continue to motivate the addition of new features in _GRworkbench_, it becomes progressively more useful as a tool for numerical investigations in General Relativity.
Figure 2: An idealised interferometer simulated in _GRworkbench_, with 5 orthogonal arms. The interferometer is orbiting the field centre, marked by the ball. The world-lines of the end-mirrors of each arm are joined to the world-line of the beam-splitter by null geodesics. | [
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|
P. S. Aspinwall, K3 surfaces and string duality, 1996 preprint, arXiv:hep-th/9611137.
J. de Boer et al., Triples, fluxes, and strings, Adv. Theor. Math. Phys. **4**, 995 (2002).
J. Gauntlett, Branes, calibrations and supergravity, in Strings and Geometry, Douglas et al., pp. 79-126, AMS 2004.
J. Li and S.-T. Yau, The existence of supersymmetric string theory with torsion, 2004 preprint, arXiv:hep-th/0411136 | [] |
|
* [6]M. S. Morris and K. S. Thorne, Am. J. Phys. **56**, 395 (1988).
* [7]L. H. Ford and T. A. Roman , Phys. Rev. D **53**, 5496 (1996). | [] |
|
whereas:
Footnote 7: In the pre-relativistic period of Hamilton the fourth quaternion unit had, of course, no relationship to physical time and was added as a common scalar to the three spatial units. With regard to the applications we are interested in, we have immediately introduced the fourth dimension as a time dimension.
\[l=ict.\] (2)
Along with the self-understood operation of addition, multiplication is the fundamental operation. This is defined by the multiplication of the unit vectors. We fix the relations:
\[\left.\begin{array}[]{c}j_{x}j_{y}=j_{z},\quad j_{y}j_{x}=-j_{x}j_{y},\quad j_ {x}j_{l}=j_{l}j_{x}=j_{x},\\ j_{x}^{2}=j_{y}^{2}=j_{z}^{2}=-j_{l}^{2}=-j_{l}\end{array}\right\}\] (3)
The remaining equations are obtained by cyclically interchanging \(x,y,z\). The fourth unit vector \(j_{l}\), in the direction of the imaginary "time axis," behaves like the ordinary unit. Thus one can also write \(j_{l}=1\); in other words, \(j_{l}\) can be ignored as a factor.
The multiplication is associative but not commutative. Instead of the simple commutative law, here we have the law:
\[GF=\overline{\overline{F}\,\overline{G}}\] (4)
or
\[\overline{GF}=\overline{F}\,\overline{G},\] (4a)
where the bar means the following: one goes over to the "conjugate" of the quaternion, that is to say one gives the spatial components -- the space part as we shall call them -- opposite sign:
\[\overline{F}=-Xj_{x}-Yj_{y}-Zj_{z}+T.\] (5)
For an arbitrary number of factors, the conjugate of the product is obtained by writing the sequence of factors in reverse order and taking the conjugate of each factor.
It is easy to see that the quantity \(F\overline{F}\) is simply a number (the spatial components = 0).
## 3 Four-dimensional rotations and quaternions
Multiplication of quaternion \(F\) by quaternion \(p\) in the sense of
\[F^{\prime}=pF\] (6) | [] |
|
\[\widetilde{p_{n}}\left(T-\sum\limits_{k=1}^{m_{n}}\theta_{\xi_{k}^{n},\eta_{k} ^{n}}\right)<\frac{1}{2n}.\]
We show that \(\{\xi_{k}^{n};1\leq k\leq m_{n},n=1,2,...\}\) is a system of generators for \(E.\)
Let \(\xi\)\(\in\)\(E,\)\(\varepsilon>0\;\)and let \(n_{0}\) be a positive integer. Since \(T\) has dense range, there is \(\eta\in E\) such that \(\;\overline{p_{n_{0}}}(\xi-T\eta)\)\(<\frac{\varepsilon}{2}.\) Let \(n=\max\{n_{0},[\frac{\overline{p_{n_{0}}}(\eta)}{\varepsilon}]+1\},\) where \([t]\) means the integer part of the positive number \(t.\) Then \(p_{n_{0}}\leq p_{n}\) and
\[\overline{p_{n_{0}}}\left(\xi-\sum\limits_{k=1}^{m_{n}}\xi_{k}^{n }\left\langle\eta_{k}^{n},\eta\right\rangle\right) \leq \overline{p_{n_{0}}}\left(\xi-T\eta\right)+\overline{p_{n_{0}}} \left(T\eta-\sum\limits_{k=1}^{m_{n}}\theta_{\xi_{k}^{n},\eta_{k}^{n}}(\eta)\right)\] \[< \frac{\varepsilon}{2}+\overline{p_{n_{0}}}\left(\eta\right) \widetilde{p_{n_{0}}}\left(T-\sum\limits_{k=1}^{m_{n}}\theta_{\xi_{k}^{n},\eta _{k}^{n}}\right)\] \[< \frac{\varepsilon}{2}+\overline{p_{n_{0}}}\left(\eta\right) \widetilde{p_{n}}\left(T-\sum\limits_{k=1}^{m_{n}}\theta_{\xi_{k}^{n},\eta_{k} ^{n}}\right)<\varepsilon.\] | [] |
|
stars counted as members of Draco by Wilkinson et al. (2004). Since some of the stars clearly are discrepant from the main body of the galaxy we further exclude some of them as interlopers. The selection is indicated by the solid and dashed lines intended to follow the overall shape of such diagrams for gravitationally bound object. The line-of-sight velocity moments, dispersion \(\sigma_{\rm los}\) and kurtosis \(\kappa_{\rm los}\), calculated from the different samples thus obtained are plotted in the right panel of the Figure. In each case we divide the data into 6 radial bins with 30 stars. We see that the results in the outer bins from which the interlopers are removed are affected dramatically and both moments are significantly reduced in value. We have assumed that the binary fraction in the stellar sample is small and its effect on the moment negligible in comparison with other uncertainties (but see the discussion in Lokas et al. 2005).
Assigning sampling errors to the moments we fit them with the models based on solutions of the Jeans equations characterized by only two constant parameters, the mass-to-light ratio in V-band, \(M/L_{V}\), and the anisotropy parameter \(\beta=1-\sigma_{\theta}^{2}/\sigma_{r}^{2}\). The remaining assumptions and adopted parameters are as in Lokas et al. (2005). The res | [] |
|
ontological "state-space" with a mere epistemological one, one clearly risks various forms "incompleteness" in the respective theory. After all, even the Copenhagen Interpretation does not go so far as to deny the physical existence of quantum system as ontological entities which go through a variety of different physically relevant manifestations. But then, by denying the very possibility of ever reaching in any theory that physical ontology, the risk is taken for "incompleteness".
In this way, one may note that the attempts within the Copenhagen Interpretation which try to connect human consciousness with the dynamics of quantum systems are to a good extent trying to support themselves through a self-fabricated entrapment within the epistemic. Namely
* *one first denies the very possibility of an ontological theory,
* *then one ends up with incompleteness, and finally
* *one has a chance to introduce some active, causal role for human consciousness during certain experimental processes, in an attempt to explain the whole range of dynamics of quantum systems.
**4. About Relative Clumsiness**
When one observes, for instance, the Moon from the Earth and does so with the naked eye, it is very hard to assume that one can cause by that any relevant disturbance in the motion of the Moon. In other words, such an experiment performed relating to the dynamics of the Moon can quite safely be considered as perfectly _non-invasive_ in terms of that dynamics.
On the other hand, as it is well known, when we implement various experiments in genetic engineering, many of our actions end up being not only invasive, but simply destructive, even if they were not meant to be so. | [] |
|
then Julius Wess and I noticed the cancellation of divergences, as well as the fact that fewer renormalization constants are needed in SUSY quantum field theories.
The SM has both boson and fermion fields, but the obvious idea to arrange them in supermultiplets fails to agree with experiment. It turns out that one is forced to introduce a new superpartner field to every single field present in the SM. And in addition one must introduce a second Higgs doublet.
Let us remember the field content of the SM
\[\begin{split}\text{Leptons}:L_{i}=\binom{v}{e}_{L_{i}}&=(1,2,-\frac{1}{2})\\ e_{R_{i}}&=(1,1,-1)\\ \text{Quarks}:Q_{i}=\binom{u}{d}_{L_{i}}&=(3,2,\frac{1}{6})\\ u_{R_{i}}&=(3,1,\frac{2}{3})\\ d_{R_{i}}&=(3,1,-\frac{1}{3})\\ \text{Higgs }:H=\binom{h^{+}}{h^{0}}&=(1,2,\frac{1}{2})\\ \end{split}\]
Here \(i=1,2,3\) is the "family" index, \(L\) and \(R\) refer to the left- and right-handed components of fermions and the numbers in parenthesis are the \(SU(3)\otimes SU(2)\otimes U(1)\) quantum numbers.
Let us now compare the field content of the SM with that of the MSSM. The rules for building \(N=1\) SUSY gauge theories are to assign a vector superfield (VSF) to each gauge field and a chiral superfield (\(\chi\)SF) to each matter field. The field content of a VSF is one gauge boson and a Weyl fermion called gaugino, and of the \(\chi\)SF is one Weyl fermion and one complex scalar. The VSF's transform under the adjoint of the gauge group, while the \(\chi\)SF's can be in any representation. Since none of the matter fields of the SM transform under the adjoint of the gauge group, we cannot identify them with the gauginos. There are additional constraints dictated by the chirality and lepton number of the SM fields. The result is that the minimal choice is to attribute to the \(\chi\)SF's of the MSSM the quantum numbers in the table. B and L are baryon and lepton number. | [] |
|
# hep-ph/yymmddd **Gauge coupling and fermion mass relations in low string scale brane models**
D.V. Gioutsos, G.K. Leontaris and J. Rizos
Theoretical Physics Division, Ioannina University, GR-45110 Ioannina, Greece
We analyze the gauge coupling evolution in brane inspired models with \(U(3)\times U(2)\times U(1)^{N}\) symmetry at the string scale. We restrict to the case of brane configurations with two and three abelian factors (\(N=2,3\)) and where _only one_ Higgs doublet is coupled to down quarks and leptons and only one to the up quarks. We find that the correct hypercharge assignment of the Standard Model particles is reproduced for six viable models distinguished by different brane configurations. We investigate the third generation fermion mass relations and find that the correct low energy \(m_{b}/m_{\tau}\) ratio can be obtained for \(b-\tau\) Yukawa coupling equality at a string scale as low as \(M_{S}\sim 10^{3}\,\) TeV.
## 1. | [] |
|
UCRHEP-T395
August 2005
**Tetrahedral Family Symmetry**
**and the Neutrino Mixing Matrix**
**Ernest Ma**
Physics Department, University of California, Riverside, California 92521, USA,
and Institute for Particle Physics Phenomenology, Department of Physics,
University of Durham, Durham, DH1 3LE, UK
###### Abstract
In a new application of the discrete non-Abelian symmetry \(A_{4}\) using the canonical seesaw mechanism, a three-parameter form of the neutrino mass matrix is derived. It predicts the following mixing angles for neutrino oscillations: \(\theta_{13}=0\), \(\sin^{2}\theta_{23}=1/2\), and \(\sin^{2}\theta_{12}\) close, but not exactly equal to 1/3, in one natural symmetry limit. | [] |
|
The ratio of \({}^{236}\)U and \({}^{235}\)U contents was evaluated by comparing the yield of the \({}^{236}\)U peak at 49.37 keV to the yield curve obtained from the yields of the 58.6, 84.2 and 90 keV peaks of \({}^{235}\)U and it was found to be \((0.67\pm 0.10)\times 10^{-2}\). Then the \({}^{236}\)U content was calculated to be \((0.51\pm 0.08)\times 10^{-2}\) g/g for the RRM.
Similarly, the 59.6 keV line was identified for \({}^{241}\)Am and its activity was calculated by peak ratio technique as above and found to be \(125\pm 15\) Bq/g for the RRM.
In the spectra of the RFM the peaks of \({}^{236}\)U and \({}^{241}\)Am could not be identified. More precisely, the upper limit of the count rates at the peaks of \({}^{236}\)U and \({}^{241}\)Am may be estimated as the statistical error of the count rate in the areas of the spectrum where these peaks should be (at 49.37 keV and at 59.6 keV). In this way, for the RFM the upper limit of the \({}^{236}\)U content was estimated to be about 0.0008 g/g, while the \({}^{241}\)Am activity in the RFM was estimated to be not more than 15 Bq/g.
## 5 Discussion
In the present paper independent NDA methods for HEU characterization are described. These methods were developed within the two-months time frame of the Round Robin Exercise organized in 2001 by the International Technical Working Group for Combating Illicit Trafficking of Nuclear Materials [3, 4]. In fact, the results for the \({}^{235}\)U content and total uranium content were included already in the 24-hours report. The results of the detailed calculations of the \({}^{234}\)U, \({}^{235}\)U, \({}^{236}\)U, \({}^{238}\)U and \({}^{232}\)U contents were used for preparing the final, two-months report, together with the results of mass spectrometric measurements. The age of the Round-Robin material determined by the method described here was also available
Figure 4: Gamma-spectrum of the Round-Robin material taken by a medium-area planar HPGe detector. | [
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HU-EP-05/35
hep-th/0508071
**D-branes in overcritical electric fields**
Harald Dorn, Mario Salizzoni and Alessandro Torrielli
Humboldt-Universitat zu Berlin, Institut fur Physik
Newtonstrasse 15, D-12489 Berlin
dorn,sali,[email protected]
**Abstract**
We collect some arguments for treating a D-brane with overcritical electric field as a well-posed initial condition for a D-brane decay. Within the field theoretical toy model of Minahan and Zwiebach we give an estimate for the condensates of the related infinite tower of tachyonic excitations.
## 1 | [] |
|
high genus, with the branch points on the complex plane being totally unresolvable when the cycles are large.
### Dynamics in the \(p\neq p^{\prime}\) case. | [] |
|
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# Dynamic rewiring in small world networks
J P L Hatchett
Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Saitama 351-0198, Japan [email protected]
N S Skantzos
Instituut voor Theoretische Fysica, Celestijnenlaan 200D, K.U.Leuven B-3001, Belgium [email protected]
T Nikoletopoulos
Department of Mathematics, King's College London, Strand WC2R 2LS, U.K. [email protected]
###### Abstract
We investigate equilibrium properties of small world networks, in which both connectivity and spin variables are dynamic, using replicated transfer matrices within the replica symmetric approximation. Population dynamics techniques allow us to examine order parameters of our system at total equilibrium, probing both spin- and graph-statistics. Of these, interestingly, the degree distribution is found to acquire a Poisson-like form (both within and outside the ordered phase). Comparison with Glauber simulations confirms our results satisfactorily.
pacs: 75.10.Nr, 05.20.-y, 89.75.-k +
Footnote †: preprint: FoG 2005/03
## I | [] |
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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
CERN-PH-EP/2005-035
15th July 2005
**Colour reconnection in \(\mathrm{e}^{+}\mathrm{e}^{-}\rightarrow\mathrm{W}^{+}\mathrm{W}^{-}\)**
**at \(\sqrt{s}=189\)-\(209\)\(\mathrm{GeV}\)**
The OPAL Collaboration
Abstract
The effects of the final state interaction phenomenon known as colour reconnection are investigated at centre-of-mass energies in the range \(\sqrt{s}\simeq 189\)-209 \(\mathrm{GeV}\) using the OPAL detector at LEP. Colour reconnection is expected to affect observables based on charged particles in hadronic decays of \(\mathrm{W}^{+}\mathrm{W}^{-}\). Measurements of inclusive charged particle multiplicities, and of their angular distribution with respect to the four jet axes of the events, are used to test models of colour reconnection. The data are found to exclude extreme scenarios of the Sjostrand-Khoze Type I (SK-I) model and are compatible with other models, both with and without colour reconnection effects. In the context of the SK-I model, the best agreement with data is obtained for a reconnection probability of 37%. Assuming no colour reconnection, the charged particle multiplicity in hadronically decaying W bosons is measured to be <nchqq> =19.38+-0.05(stat.)+-0.08(syst.).
(Sbmitted to Eur. Phys. J. C) | [] |
|
nch solution in all cases.
## 5 Conclusions
We have shown that the nonextremal shell branch enhancon solution is physical when the nonextremality parameter \(r_{0}\) is small enough. We have also shown that a supergravity solution of the form given in (6) - (10) exists for all masses above the ADM mass of the extremal enhancon. The nonextremal enhancon whose mass is close to that of the extremal enhancon should take the form of the shell branch solution, because no horizon branch solution exists. This was to be expected because the shell branch solution tends to the extremal solution in the extremality limit \(r_{0}\to 0\). However, the solution for a nonextremal enhancon with a large ADM mass takes the form of the horizon branch solution, because the shell branch solution is unphysical in this region of the parameter space. This was also to be expected because the object with large mass should behave like a black hole, and should therefore have a horizon, as was discussed in ref. [4].
Having identified the form of the nonextremal enhancon solution it would be interesting to return to the questions of stability that were addressed in refs. [3] and [4]. Since the shell branch solution is valid for smaller masses, and the horizon branch for larger masses, we expect a transition from the horizon branch to the shell branch at some value of \(r_{0}\). The stability of the horizon branch solution was tested in refs. [3] and [4], but no instabilities were found. However the results we have described | [] |
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|
where the right-hand side is evaluated at the value of \(\phi\) corresponding to horizon crossing for the comoving scale of interest. With a power-law potential
\[V(\phi)=\lambda\phi^{n},\] (17)
this gives, neglecting logarithmic factors (see, e.g., [22]),
\[Q\propto\lambda^{1/2}.\] (18)
Suppose now that \(\lambda\) is a variable, which may be determined by some additional scalar field. It seems natural to assume that the range of variation for \(\lambda\) is \(\Delta\lambda\sim 1\). The observed value of \(\sigma_{G}\) is obtained for \(\lambda\sim 10^{-14}\), and the anthropic range (11) corresponds to \(10^{-16}\lower 2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}\lambda\lower 2.1527 7pt\hbox{$\;\buildrel<\over{\sim}\;$}10^{-12}\). Since this range is so narrow, Graesser _et. al._[11] argue that the same logic we used for the cosmological constant implies that the prior for \(\lambda\) should be nearly flat in the range of interest,
\[dP_{prior}/d\lambda\approx{\rm const}.\] (19)
Then it follows from (18) that \(dP_{prior}(Q)\propto QdQ\), and Eq. (15) gives
\[dP(Q)\propto Q^{4}dQ.\] (20)
This distribution is strongly biased in favor of large values of \(Q\). If anthropic factors cut off the distribution above \(Q^{(max)}\sim 10^{-4}\), then Eq. (20) suggests that this cutoff value is \(10^{5}\) times more probable than the observed value \(Q\sim 10^{-5}\). This is the large \(Q\) catastrophe.
We note, however, that there is an important difference between the cosmological constant and the inflaton self-coupling \(\lambda\), which may invalidate the argument for the flat prior (19). Unlike the small cosmological constant, the value of \(\lambda\) has a strong effect on the dynamics of inflation. As we shall see later, smaller values of \(\lambda\) give larger inflationary expansion factors. Hence, \(\lambda=0\) is a rather special value of the coupling, and the flat prior assumption is not justified. | [] |
|
[27] V. Vanchurin, A. Vilenkin and S. Winitzki, Phys. Rev. **D61**, 083507 (2000).
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|
\(S-T\) relations.[25] RDCS J1252 appears thus well thermalized with thermodynamical properties similar to those of clusters at low redshift. The value of the metallicity obtained from the XMM spectroscopic data[26] turns out to be consistent with the mean ICM metallicity value for lower redshift clusters.[28] This result thus provides further support for the lack of evolution of the amount of metals in galaxy clusters up to \(z\simeq 1.3\) and is consistent with the major episode of metal enrichment occurring at \(\sim 3\). The total mass of the cluster is estimated to be \((1.9\pm 0.3)\times 10^{14}M_{\odot}\) within a radius of 536 kpc,[26] consistent with the \(\sigma-M\) relation predicted by Bryan & Norman (1998).[55] In general, the structure and physical properties of RDCS J1252's ICM show that this cluster is a massive system in an advanced thermodynamical state, with scale properties similar to those of clusters at low redshift, that we are observing at a lookback time of 8.5 Gyrs (when the universe was about 36% of its present age).
Figure 2: RDCS J1252. **a)** ACS weak lensing mass map (taken from Lombardi et al. 2005) centered on the optical center of the cluster and covering 5.7 \(\times\) 5.7 arcmin\({}^{2}\). The dashed square has a side length of 2 arcmin (1 Mpc at the cluster redshift). **b)** Chandra X-ray iso-contours in the central 2 arcmin of the cluster (dashed square; taken from Lombardi et al. 2005). **c)** Map of the smoothed K-band light of photometric member galaxies. The circle marks the central 130 arcseconds diameter region of the cluster; taken from Toft et al. (2004). **d)** The 0.6 \(\times\) 0.6 arcmin\({}^{2}\) ACS optical image of the cluster core, dominated by two elliptical galaxies. In all panels North is up and East is left. The distributions of DM, gas and cluster members (K-band light) are elongated in the East-West direction. | [
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## V Internal dipolar field nonhomogeneity _vs._ comb and bulk-dead modes
Now let's superimpose the calculated magnetostatic mode frequency spectrum and the profile of local field \(H(n)\) plotted along the rod axis (Fig. 4). A strong spatial inhomogeneity of the local field is apparent from the calculated field values; two regions, qualitatively distinct in terms of inhomogeneity, can be distinguished: outer regions, with steep profile bias indicating high local field gradient, and a central region, in which the profile bias is relatively mild. Note also that the average value of local field, \(H_{av}\), can be regarded as the border line between these two regions. The mode profiles, ordered by growing frequency, are superimposed on the local field curve, with energy scale (on the vertical axis) maintained (_i.e._ common for the mode frequencies \(H_{m}\) and the local field profile \(H(n)\)). An interesting correlation occurs between the mode type and the position of the mode frequency with
Figure 3: Numerically calculated magnetostatic mode profiles in a rod of length 200\(a\) depicted along the central axis (indicated in Figure 1) showing separately: (a) the dynamical magnetization \(m^{+}\) relative values, and (b) the corresponding absolute values, \(|m^{+}|\). | [
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* [11] G. Ortiz, R. Somma, H. Barnum, E. Knill and L. Viola, _Entanglement as an observer-dependent concept: an application to quantum phase transitions_, quant-ph/0403043 v1 4 Mar 2004.
* [12] E. Schrodinger, _Die gegenwartige Situation in der quantenmechanik_, _Naturwissenschaften_**23** (1935), 823, 844.
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* [16]Bohm [14] uses the term correlated in a different sense for the classical case.
* [17] This phrase is attributed to Einstein. See _The Born-Einstein Letters_, with comments by M. Born, Walker, New York (1971), referred to in N. D. Mermin, _Is the moon really there when nobody looks? Reality and the quantum theory_, Physics Today/April, pg.38 (1985).
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* [19] N. Birge, private comm. (2004).
* [20] T. A. Kaplan and C. Piermarocchi, _Spin Swap and \(\sqrt{SWAP}\) vs. Double Occupancy in Quantum Computation_, in Proc. of INDO-US Workshop, "Nanoscale Materials: From Science to Technology", Puri, India, April 5-8, 2004, to appear.
* [21] T. A. Kaplan and C. Piermarocchi, _Spin swap vs. double occupancy in quantum gates_, _Phys. Rev. B_ **70** (2004), 161311(R) .
* [22] T. A. Kaplan, unpublished work. | [] |
|
Y. F. was supported in part by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science, and Technology of Japan (17740162). T. K. S. is financially supported by the JSPS Research Fellowship for Young Scientists, grant 4607. | [] |
|
# Diquark-diquark correlations in the \({}^{1}S_{0}\)\(\Lambda\Lambda\) potential
T. Fernandez-Carames\({}^{(1)}\)
A. Valcarce\({}^{(2)}\)
and P. Gonzalez\({}^{(1)}\)
\((1)\) Dpto. de Fisica Teorica and IFIC
Universidad de Valencia - CSIC, E-46100 Burjassot, Valencia, Spain \((2)\) Grupo de Fisica Nuclear and IUFFyM
Universidad de Salamanca, E-37008 Salamanca, Spain
###### Abstract
We derive a \(\Lambda\Lambda\) potential from a chiral constituent quark model that has been successful in describing one, two and three nonstrange baryon systems. The resulting interaction at low energy is attractive at all distances due to the \(\sigma\) exchange term. The attraction allows for a slightly bound state just below the \(\Lambda\Lambda\) threshold. No short-range repulsive core is found. We extract the diquark-diquark contribution that turns out to be the most attractive and probable at small distances. At large distances the asymptotic behavior of the \(\Lambda\Lambda\) interaction provides a prediction for the \(\sigma\Lambda\Lambda\) coupling constant.
Keywords: diquarks, chiral constituent quark models, \(\Lambda\Lambda\) interaction
Pacs: 12.39.Jh, 12.39.Pn, 14.20.Pt | [] |
|
# Thermal Radiation from Au + Au Collisions at \(\sqrt{s_{NN}}=200\) GeV Energy
Jan-e Alam\({}^{a}\), Jajati K. Nayak\({}^{a}\), Pradip Roy\({}^{b}\), Abhee K. Dutt-Mazumder\({}^{b}\) and Bikash Sinha\({}^{a,b}\)
\(a\) Variable Energy Cyclotron Centre, 1/AF Bidhan Nagar, Kolkata 700 064, INDIA
\(b\) Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar Kolkata 700 064, INDIA
###### Abstract
The transverse momentum distribution of the direct photons measured by the PHENIX collaboration in \(Au+Au\) collisions at \(\sqrt{s_{NN}}=200\) GeV/A has been analyzed. It has been shown that the data can be reproduced reasonably well assuming a deconfined state of thermalized quarks and gluons with initial temperature more than the transition temperature for deconfinement inferred from lattice QCD. The value of the initial temperature depends on the equation of state of the evolving matter. The sensitivities of the results on various input parameters have been studied. The effects of the modifications of hadronic properties at non-zero temperature have been discussed.
pacs: 12.38.Mh,25.75.-q,25.75.Nq,24.10.Nz | [] |
|
## 5 Conclusion and discussion
A new alternative tool, the SFPM Model, to evaluate scientific and financial performances has been discussed. In the model, a simultaneous relation between scientific and financial performances has been formulated assuming that the quantitative scores should be extracted only from the scientific outcomes. The model solves a crucial problem on how to measure simultaneously both scientific and financial performances of scientific activities in various fields. It provides a simple tool for immediate evaluation which is in practical daily management urgently needed. Since the model is based on the completely quantitative measurements, it could avoid any ambiguities and then guarantees the objectiveness of evaluation process. A sustainable evaluation utilizing the model could also measure and integrate long-term scientific and financial performances in complement with the other known evaluation methods.
Here, I list several advantages of measurement tool based on the SFPM Model,
* *Since it is based only on the scientific outcomes, the objectivity and transparency of measurement can be guaranteed.
* *A single year base method makes the evaluation process and decision-making for next fiscal year easier, since the result reflects an up-to-date real condition.
* *In long term, the whole annual evaluations of each fellow can be compiled to implement better compensation system. For example, the evaluation result | [
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Inference_ (Prentice Hall, New Jersey, 1997), 5th ed.
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* Javanainen and Ivanov (1999) J. Javanainen and M. Y. Ivanov, Phys. Rev. A **60**, 2351 (1999).
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* Carr et al. (2005) L. D. Carr, M. J. Holland, and B. A. Malomed, J. Phys. B **38**, 3217 (2005). | [] |
|
.
* [10] R. G. Newton. _Scattering Theory of Waves and Particles_. Springer Verlag, N. Y., 1982.
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|
\[I=\left|\int_{\mathbb{S}^{4}}(u_{1}u_{2})\times(1-\Delta)^{-{\alpha}}(u_{3}u_{ 4})\,dx\right|\ .\] | [] |
|
This bound shows that all variable-\(r\)-bonacci sequences are \(O(2^{n-1})\). That is, at worst exponential order.
The following lemma is the basis for many of our other estimates. We relate the growth of \(b(n)\) to \(r(n)\).
**Lemma 2.7****.**: _For all \(n\geq 1\),_
\[\frac{b(n)}{b(n-1)}\leq r(n).\]
Proof.: \[b(n) =\sum_{k=1}^{r(n)}b(n-k)\] \[\leq\sum_{k=1}^{r(n)}b(n-1)\qquad\text{since the $b(n)$ are non-increasing,}\] \[=r(n)b(n-1).\]
The above estimate is sharp. For any \(n>1\), let \(r(1)=\cdots=r(n-1)=1\) and \(r(n)=n\). Then \(b(1)=\cdots=b(n-1)=1\), and \(b(n)=n\), so \(b(n)/b(n-1)=n=r(n)\).
**Corollary 2.8****.**: _For all \(n,m\geq 1\)_
\[\frac{b(n+m)}{b(n)}\leq\prod_{k=n+1}^{n+m}r(k).\]
Proof.: Write \({b({n+m})}/{b(n)}\) as a telescoping product, and apply Lemma 2.7\(m\) times:
\[\frac{b({n+m})}{b(n)}=\prod_{k=n+1}^{n+m}\frac{b(k)}{b({k-1})}\leq\prod_{k=n+1 }^{n+m}r(k).\]
From the above estimate, it follows that \(b(n)\leq\prod_{k=1}^{n}r(k)\). Which implies \(b(n)\leq n!\). However, from Lemma 2.6 we know in fact that \(b(n)\leq 2^{n-1}\). So while Lemma 2.7 gives a sharp estimate of the short term growth of \(b(n)\), in the long term it is highly inaccurate. However, we only use the above corollary to obtain lower bounds on growth, so the inaccuracy is somewhat reduced. We state the reciprocal of it for reference. | [] |
|
+
Footnote †: preprint: hep-th/0508133, MIT-CTP-3673
###### Contents
Contents
## 1 Introduction
Since the early days of string theory, it has been clear that there are many possible ways in which to compactify the various perturbative superstring and supergravity theories from ten or eleven dimensions to four space-time dimensions. For example, compactifying any ten-dimensional string theory on a Calabi-Yau complex three-fold leads to a supersymmetric theory of gravity coupled to light fields in the remaining four macroscopic space-time dimensions. Moduli parameterizing the size and shape of the Calabi-Yau appear as massless scalar fields in the four-dimensional theory. Understanding and classifying the range of possible compactifications is an important part of the program of relating superstring theory to observed phenomenology and cosmology. In recent years, compactifications with topologically quantized fluxes wrapping compact cycles on the compactification manifold have become a subject of much interest, following the work of [1, 2, 3]. The topological fluxes produce a potential for the scalar moduli, and can thus "stabilize" some or all of the moduli to take specific values [4, 5, 6]. Once fluxes are added to the system, however, the geometric structure of the compactification manifold may also become more general. Recent work has addressed the generalization to superstring compactifications on non-Calabi-Yau geometries [7, 8, 9, 10]. | [] |
|
### Comparison of numerical and CSS critical solutions
If our numerical scheme works properly we should obtain the same critical solutions as we did by using the CSS ansatz (up to a truncation error). We must bear in mind, however, that the CSS critical solutions do not describe an asymptotically flat spacetime whereas the spacetime generated numerically is asymptotically Schwarzschild and therefore the solutions match only in a limited domain close to \(r=0\). In order to compare the solutions we have to translate the coordinate \(r\) used in numerical calculations into the self similar coordinate \(x\) in which the CSS solutions are cast. The relation is provided by the equation (3.3). Since the relation of \(t_{*}\) to \(t\) is not known we use some distinct feature of the solution, e.g., local minimum or maximum to identify a particular \(r\) with a particular \(x\). This allows us to calculate \(t_{*}\).
Figures 3-6 show the comparison for \(k^{2}=10^{-6}\). The numerical data were taken from the closest subcritical run just before the fluid dispersed. The numerical solutions agree very well with the CSS ones in a limited region as expected. The results for other values of \(k\) agree similarly well.
Note that the lapse \(\alpha\) used in the numerical calculations is not the same as the \(\alpha\) from equation (3.4). Therefore in order to compare the functions \(N(x)\) we must rescale one by a constant factor -- we simply matched the leftmost data point from the numerical calculations with the corresponding one from the CSS solution. The dotted line shows the AMR hierarchy level. An increase in hierarchy level by one corresponds to a reduction of the cell size by factor of \(2\). | [
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\(\sigma^{2}=0.87\). The noisy region of the spectrum is characterized by the values \(\tilde{\lambda}_{min}=0.78\) and \(\tilde{\lambda}_{max}=0.99\). With these values one would conclude that \(19\) eigenvalues contain economic information. This is quite surprising because one would expect that for a short time horizon the correlation coefficients are less influenced by economic sectors than when one considers daily returns. We will see in the following sections that clustering methods support this view.
Figure 8 shows the components \({u}^{1}_{i}\) of the first eigenvector. In the x axis of this figure the stocks are sorted in decreasing order according to the total number of trades recorded in the investigated period. The figure shows that the most heavily traded stocks have a larger component in the first eigenvector. This behavior is not observed in the first eigenvector for daily returns.
A possible interpretation of this result is the following. Suppose that, as a first approximation, the dynamics of the set of stocks is described by a one factor model, i.e. a model in which the dynamics of each variable is
Figure 7: PMFG obtained from daily returns of a set of 92 stocks traded in the LSE in 2002. Black circles are identifying stocks belonging to the Financial sector. Gray circles are identifying stocks belonging to the Services sector. Other stocks are indicated by empty circles. Black thicker lines are connecting stocks belonging to the Financial sector. Gray thicker lines are connecting stocks belonging to the Services sector. | [
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* [13] F. Panaite, Hopf bimodules are modules over a diagonal crossed product algebra, Comm. Algebra**30** (2002), 4049-4058.
* [14] F. Panaite, F. Van Oystaeyen, L-R-smash product for (quasi) Hopf algebras, arXiv:math.QA/0504386. | [] |
|
We have
\[\frac{b(N+1)}{N+1} =\frac{b(N+1)}{b(N)}\frac{b(N)}{N}\frac{N}{N+1}\] \[\geq(2)(L-\varepsilon)(1-\varepsilon),\] \[=2L+O(\varepsilon).\]
by Lemma 2.3, condition 4, and condition 3 respectively. So,
\[\left|\frac{b(N+1)}{N+1}-L\right|\geq 2L+O(\varepsilon)-L=L+O(\varepsilon).\]
But by condition 4, we have
\[\left|\frac{b(N+1)}{N+1}-L\right|<\varepsilon\ll L.\]
Therefore, \(L=0\).
We can have slower than polynomial growth. No other known Fibonacci-type sequence grows so slowly.
**Example 3.9****.**: _For \(n\geq 2\), let \(r(n)=2\) if \(n=2^{2^{k}}\) for some \(k\in{\mathbb{Z}}\), and \(r(n)=1\) otherwise._
\[\begin{array}[]{|c|c|c|c|c|c|c|}\hline\cr n&0&1&2&4&16&256\\ \hline\cr r(n)&1&1&2&2&2&2\\ \hline\cr b(n)&1&1&2&4&8&16\\ \hline\cr\end{array}\]
_It is easy to show that \(b(n)\) is \(\Theta(\log_{2}n)\)._
Similarly, we can construct examples that are \(\Theta(\log_{2}\log_{2}n)\), etc. Thus \(b(n)\) can grow quite slowly indeed.
## 4 Generalization
We define a generalization of \(b(n)\). This generalization allows us to pick different initial conditions for our sequence. It also allows us to remove the restrictions that \(r\) be sublinear. | [] |
|
\(DSP>6.9\), respectively. The same limits for \({\rm SNR}_{\rm OOTV}\) are \(SNR>5.5\) and \(SNR>6.6\). Obviously, feasible transit candidates are those events that show high DSP, but \({\rm SNR}_{\rm OOTV}\) is low. The above values justify the use of our "soft" cutoffs (meaning that we do not even loose marginal candidates) of \({\rm DSP}>6.0\) and \({\rm SNR}_{\rm ootv}<7.0\) for transit selection in this sample.
4. Results
4.1 Distribution of the OOTV peak frequencies
Fig. 2 shows that most of the peak frequencies of the Fourier spectra of the OOTVs are grouped around integer frequencies (in the units of the orbital frequency), indicating that tidal and/or reflection effects are the dominating factors in causing OOTV. Some 75% of the stars exhibit OOTV with peak frequencies \(n\pm 0.2\).
4.2 Orbital frequency vs. \(Q_{\rm tran}\)
The left panel in Fig. 3 shows the \(Q_{\rm tran}\) values derived for the full sample of 2495 stars without applying any parameter cuts. The right panel shows the result after the application of the DSP and \({\rm SNR}_{\rm OOTV}\) cutoffs. There remain only 18 stars satisfying both of these cuts and the \(Q_{\rm tran}<1.1Q_{\rm tran,G0V}\) constraint, where \(Q_{\rm tran,G0V}\) is the estimated fractional transit time with a G0V primary. (The factor \(1.1\) is used for rough error allowance in the \(Q_{\rm tran}\) values). | [
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* [Para] A. E. Parker, _Good \(l\)-filtrations for \(q\)-\(\mathrm{GL}_{3}(k)\)_, preprint.
* [Parb] by same author, _Higher extensions between modules for \(\mathrm{SL}_{2}\)_, preprint.
* [Par01] by same author, _The global dimension of Schur algebras for GL\({}_{2}\) and GL\({}_{3}\)_, J. Algebra **241** (2001), 340-378.
* [Par03] by same author, _On the Weyl filtration dimension of the induced modules for a linear algebraic group_, J. reine angew. Math. **562** (2003), 5-21.
* [PS05] B. J. Parshall and L. L. Scott, _Quantum Weyl reciprocity for cohomology_, Proc. London Math. Soc. **90** (2005), 655-688.
* [RH03] S. Ryom-Hansen, _Appendix. Some remarks on Ext groups_, J. reine angew. Math. **562** (2003), 23-26.
* [Sch01] by same author, _Uber eine Klasse von Matrizen, die sich einer gegebenen Matrix zuordnen lassen_, I. Schur: Gesammelte Abhandlungen (A. Brauer and H. Rohrbach, eds.), vol. I, Springer-Verlag, 1973, pp. 1-71.
* [Sch27] I. Schur, _Uber die rationalen Darstellungen der allgemeinen linearen Gruppe_, I. Schur: Gesammelte Abhandlungen (A. Brauer and H. Rohrbach, eds.), vol. III, Springer-Verlag, 1973, pp. 68-85.
* [Tot97] B. Totaro, _Projective resolutions of representations of GL\((n)\)_, J. reine angew. Math. **482** (1997), 1-13.
* [Wen89] Wen Kexin, _The composition of intertwining homorphisms_, Comm. Alg. **17** (1989), 587-630. | [] |
|
work is shown in Fig. 5. Closed squares represent the numerical results and the solid line is a fit
Figure 4: Plots of \(\rho\) vs \(\lambda\) in the WS (a) and \(\rho\) vs \(1/\lambda\) in the BA (b) networks under different values of the degree-dependent delay time. Parameter values (from bottom to top) \(\alpha=0.15\), \(0.25\), \(0.35\), and \(0.45\), respectively.
Figure 5: The plot of the epidemic threshold \(\lambda_{c}\) as a function of the tunable parameter \(\alpha\) in the WS network. The solid line is a fit to the form \(\lambda_{c}(\alpha)\sim E+F\alpha\). | [
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### The BHPS model
A simple model for the \(x\)-dependence of charm can be obtained by neglecting the \(p_{\perp}\) content, the \(1/x_{j}\) factors, and \(F^{2}\) in Eq. (1). Further approximating the charm quark mass as large compared to all the other masses yields
\[dP\propto\prod_{j=1}^{5}dx_{j}\,\delta(1-\sum_{j=1}^{5}x_{j})\,(1/x_{4}+1/x_{5 })^{-2}\;,\] (3)
where \(x_{4}=x_{c}\) and \(x_{5}=x_{\bar{c}}\). Carrying out all but one of the integrals and normalizing to an assumed total probability of \(1\%\) yields
\[{{dP}\over{dx}}=f_{c}(x)=f_{\bar{c}}(x)=6\,x^{2}\left[6\,x\,(1+x)\,\ln x\,+\,( 1-x)(1+10x+x^{2})\right]\;,\] (4)
where \(x=x_{c}\) or \(x_{\bar{c}}\,\). Equation (4) was first derived by Brodsky, Hoyer, Peterson and Sakai [6], and has been used many times since. We will use this BHPS model as a convenient reference for comparing all other models.
Charm distributions that arise when the transverse momentum content of Eq. (1) is not deleted are derived in the following subsections.
### Exponential suppression
A plausible conjecture would be that high-mass configurations in Eq. (1) are suppressed by a factor
\[F^{2}=e^{-(s-m_{0}^{\,2})/\Lambda^{2}}\;.\] (5)
Figure 1: Momentum distribution of \(c\) or \(\bar{c}\) from the 5-quark model with the exponential suppression of Eq. (5) (left), or the power-law suppression of Eq. (6) (right). Solid curves are the BHPS model of Eq. (4). All curves are normalized to \(1\%\) integrated probability. | [
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the number of sums is the same than that of fluctuating extensive variables). For an ergodic system, for which \(\mathcal{N}(\Upsilon_{i})=\Upsilon_{i}\), this leads to the generalized Gibbs distribution
\[\Upsilon=\sum_{i}\Gamma_{i}e^{-\sum_{k}y_{k}X_{k,i}}\] (35)
and, in the non-ergodic case with fractal phase space (N(Ui)=Uid)
\[\Upsilon=\sum_{i}\Gamma_{i}\left(1-(1-d)\sum_{k}y_{k}X_{k,i}/\Gamma_{i}^{1-d} \right)^{\frac{1}{1-d}}\] (36)
## 6 Conclusions
The unifying principle of the smooth phase space evolution Eq. (32) allows to build a generalized thermostatistic formalism concerning macrovariables analogously to that of Hamiltonian mechanics containing microvariables (comparison of Eqs. (5) with (31) makes explicit this analogy: the role played by \(\mathcal{X}\) in macroscopic systems is quite similar to the one played by \(H\) in microscopic ones). It is to be noted that this principle embodies the maximum entropy principle in the microcanonical ensemble as well as the minimum of the conventional thermodynamic potentials at equilibrium (a maximum of their closely related Massieu-Planck entropic potentials, see Table 1) for each ensemble. This is clearly seen in the differential equation which serves as definition of the entropy Eq. (14), since in the microcanonical ensemble \(1/\mathcal{N}(\Gamma)\) is directly related to probability. As probability is a positive quantity which decreases with increasing the available phase space (of course, this applies far from phase separation) entropy is here, therefore, a _concave and increasing_ function of its argument. The generalized Massieu-Planck entropic potential \(\mathcal{X}\) describes all the thermodynamics of a given system when known as a function of the natural variables and is the key stone, in our view, in connecting | [] |
|
\pm 1/\sqrt{a}\) (stable).
Consider Eq. (25) near a stable fixed point by the change \(y\to w+1/\sqrt{a}\). Then
\[D^{\alpha}w+2w+3\sqrt{a}w^{2}+aw^{3}=0\,.\] (26)
Close to the stable fixed point we have a linear equation
\[D^{\alpha}w_{0}+2w_{0}=0\] (27)
with a solution
\[w_{0}(t)=BE_{\alpha}(-2t^{\alpha})\,,\] (28)
and \(B\) is a constant. For \(\alpha=2-\varepsilon\) and \(\varepsilon\ll 1\) expression (28) is well approximated by the relation
\[w_{0}(t)\approx\frac{2B}{2-\varepsilon}e^{\,-\sqrt{2}\gamma t}\cos(\sqrt{2}\,t )+\mathit{O}(\varepsilon^{2}).\] (29)
Figure 1: Rate decay of the linear fractional oscillation with initial conditions \(x(0)=1\), \(x^{\prime}(0)=0\) and the index \(\alpha=1.95\), \(f_{1.95}(0)=-0.0256\). Solid line corresponds to the solution (18), dash-line - to the approximation (23) | [
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|
* *It computes the branching ratios into two particle final states (quarks and leptons, all possible combinations of gauge and Higgs bosons, charginos, neutralinos, but not decays into squarks and sleptons) of all 6 Higgs particles of the NMSSM. Three body decays via \(WW^{*}\) and \(ZZ^{*}\) are computed as in HDECAY [10], but no four body decays are taken into account.
* *It checks whether the Higgs masses and couplings violate any bounds from negative Higgs searches at LEP, including many quite unconventional channels that are relevant for the NMSSM Higgs sector. It also checks the bound on the invisible \(Z\) width (possibly violated for light neutralinos). In addition, NMHDECAY 1.1 checks the LEP bounds on the lightest chargino and on neutralino pair production.
* *It checks whether the running Yukawa couplings \(\lambda\), \(\kappa\), \(h_{t}\) or \(h_{b}\) encounter a Landau singularity below the GUT scale.
* *Finally, NMHDECAY 1.1 checks whether the physical minimum (with all vevs non-zero) of the scalar potential is deeper than the local unphysical minima with vanishing \(\left<H_{u}\right>\), \(\left<H_{d}\right>\) or \(\left<S\right>\).
The improvements in the versions 2.0+ are as follows:
1. 1.Further radiative corrections are added in the Higgs sector, in order to improve the precision of the Higgs masses calculations. In addition, all squark and slepton masses (and mixing angles for the third generation) are computed.
2. 2.Branching ratios of all Higgs states into squarks and sleptons are computed, and squark and slepton loops are included in the Higgs decays to two gluons and two photons.
3. 3.Experimental constraints from LEP and Tevatron on squark, gluino and slepton masses are checked.
4. 4.The dark matter relic density can be computed, via a call of a NMSSM version of MicrOMEGAs (that is provided on the same web site).
5. 5.The branching ratio \(BR(b\to s\gamma)\) is computed to lowest order.
6. | [] |
|
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|
# A Data Exchange Standard for Optical
(Visible/IR) Interferometry
T. A. Pauls
Naval Research Laboratory, Code 7210, 4555 Overlook Avenue SW, Washington, DC USA 20375-5351 [email protected]
Footnote 1: affiliation: We request that comments and suggestions related to the OI Exchange Format be directed to the OLBIN email list (see http://listes.obs.ujf-grenoble.fr/wws/info/olbin for information on how to subscribe and post to the list).
J. S. Young
Astrophysics Group, Cavendish Laboratory, Madingley Road, CB3 0HE, UK [email protected]
W. D. Cotton
NRAO, 520 Edgemont Road, Charlottesville, VA USA 22903 [email protected]
J. D. Monnier
University of Michigan, Department of Astronomy, Ann Arbor, MI USA 48109 [email protected] | [] |
|
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|
The language evolution presented in Figure 13 (time from left to right) shows how a metastable state is reached, where three languages survive. The state shown in the right picture survives for some time, but ultimately the upper language is able to completely eliminate the lower two ones, because it initially occupies twice the area of the other languages, and due to the interaction rules the probability for switching to another language is proportional to the area this language occupies.
More interesting in this case is that the final state of the simulation depends on the Hamming distance between the three initial languages. In Figure 13, the Hamming distance between any two of the initial languages was equal to two. By changing only the bitstring describing the upper language, so that the Hamming distance between it and the lower-left one was equal to one, while the distance to the lower-right language became three, we obtained the evolution from Figure 14, where in the final state, two languages survived instead of one.
If the language in the lower-left quarter of the plane is close in terms of the Hamming distance to the language in the upper half-plane, these two eliminate the third language and coexist as a stable state. As explanation for the extinction of the third language in Figure 14, we note that the upper and lower-left coincide within the range of mutations if the Hamming distance is small. An individual "living" at the confluence of the three languages, is going to be biased toward changing its language to the upper population, because that is predominant within its interaction range. In the next time-step, only a one-bit mutation can make this individual switch to the lower-left language, while one time-step is not enough for it to mu
Figure 12: Simulation of the coexistence of three languages.
Figure 13: Simulation of three languages coexisting as a metastable state. | [
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erformed for some values of \(\rho\) as indicated in the figure. For all \(\rho\) examined the data show a power-law behavior \(N\propto\ell^{d_{f}}\). We find \(2<d_{f}<4\), the full set of \(d_{f}\) is shown in Table 1. Two limit cases are interesting. The limit \(\rho\to 1\), which corresponds to the square lattice, has \(d_{f}\to 2\) as it is expected in a bidimensional space. The opposit limit \(\rho\to 0\), which is associated with very anisotropic structures, shows large \(d_{f}\). We cannot affirm that \(4\) is an asymptotic threshold, further numerical investigation should test this hypothesis. We remark that the \(Q_{mf}\) network does not follow a small world relationship \(\ell\propto\ln N\) that is common to most of power-law and random like networks.
An analysis of the clustering coefficient, \(C\), versus network size, \(N\), is shown in Fig. 5. The general view of this figure points to a stable behavior of \(C\) in the limit of large \(N\). The dispersion of \(C\) among \(\rho\) is not large, the numerics show \(C=0.37\pm 0.01\). Smaller values of \(\rho\), however, show a significant larger \(C\). The discussion about \(C\) is intriguing once we compare the numerical values of \(C\) with the clustering coefficient of a random network associated to the \(Q_{mf}\) network. An associated random network is defined as a network with the same \(N\) and \(<k>\) of the original network (we do not compare our results with a random network with a same \(P(k)\) because such random network would alterate the space filling characteristics that we are interested in). For a random network \(C=<k>/N\), in the case of our network: \(<k>\) is a constant number smaller than \(6\) and \(N\) a number that can grow without limit. As a consequen
Figure 4: In (a) it is displayed the average distance \(\ell\) as a function of N for several values of \(\rho\). | [
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**Searching for effects of Spatial Noncommutativity via a Penning Trap**
Jian-Zu Zhang\(\;{}^{\ast}\)
Institute for Theoretical Physics, East China University of Science and Technology, Box 316, Shanghai 200237, P. R. China
###### Abstract
The possibility of testing spatial noncommutativity via a Penning trap is explored. The case of both space-space and momentum-momentum noncommuting is considered. Spatial noncommutativity leads to the spectrum of the orbital angular momentum of a Penning trap possessing fractional values, and in the limits of vanishing kinetic energy and subsequent vanishing magnetic field, this system has non-trivial dynamics. The dominant value of the lowest orbital angular momentum is \(\hbar/4\), which is a clear signal of spatial noncommutativity. An experimental verification of this prediction by a Stern-Gerlach-type experiment is suggested.
\({}^{\ast}\) E-mail address: [email protected] | [] |
|
\[T(u_{1},v_{1},u_{2},v_{2})=V(u_{1},v_{1})\,V(u_{2},v_{2})\,V^{*}(u_{1}+u_{2},v _{1}+v_{2})\,.\] (3)
### Noise model for triple product
The data are assumed to be complex triple products averaged over a large number of "exposures". In such a case, the noise can be fully described in terms of a Gaussian noise ellipse in the complex plane. Photon, detector and background noise tend to lead to noise ellipses that are close to circular. On the other hand, fluctuating atmospheric phase errors across telescope apertures typically cause fluctuations in the amplitude of the triple product which are much larger than the fluctuations in the phase. Thus the "atmospheric" contribution to the noise ellipse is elongated along the direction of the mean triple product vector in the Argand diagram, as shown in Fig. 1. Such noise needs to be characterised in terms of the variance \(\sigma_{\perp}^{2}\) perpendicular to the mean triple product vector and the variance \(\sigma_{\parallel}^{2}\) parallel to \(T\). We can parameterize the perpendicular variance in terms of a "phase error" \(\sigma_{\theta}=(180/\pi)(\sigma_{\perp}/|T|)\). The phase error gives an approximate value for the rms error in the closure phase in degrees. We denote \(\sigma_{\parallel}\) as the "amplitude error".
In many cases, the observer may be interested primarily in the closure phase and not the triple product amplitude, and therefore may choose not to calibrate the amplitude. Such a case can be indicated in the above notation as an infinite amplitude error and a finite phase error. The data format specifies that such a case should be indicated by a NULL value for the amplitude (the amplitude error value is then ignored).
### Noise model for complex visibility
There was much discussion on the (now defunct) [email protected] email list of the representation to use for complex visibilities in the standard. A number of | [] |
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|
balances the interfacial tension cost of expanding the region between particles. It seems likely that a related transition is occurring here as we slowly reduce the interfacial tension and internal volume.
We suggested above that puncturing of the droplet surface may have led to the observed deflation. We have associated other observations with droplets retaining their integrity to higher temperatures. In figure 3 it is shown that droplets with a complete coverage of particles will eventually shatter. This effect is often seen in the thin side walls of emulsion droplets; however it is most visually dramatic to observe the fracture in the end face of a droplet. The cracking reveals the solidity of these particle layers. The layers are sufficiently rigid that they fracture rather than distort.
Figure 3: Images of a heptane-in-methanol droplet cracking. Beginning in the top left-hand corner, there is one frame every 30 seconds with each 1\({}^{\circ}\)C higher in temperature than the previous. The bulk demixing temperature is in the middle of this sequence. The images are at a depth of 40 \(\mu\)m from the surface of the holder and are roughly 120 \(\mu\)m on an edge.
Figure 2: Images of a heptane-in-methanol droplet deflating. Beginning in the top left-hand corner, there is one frame every 60 seconds with each 2\({}^{\circ}\)C higher in temperature than the previous. The bulk demixing temperature is just before the end of this sequence. The images are at a depth of 40 \(\mu\)m from the surface of the holder and are roughly 300 \(\mu\)m on an edge. | [
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Figure 3: (a) Plot of the leading edges of five detected pulses with varying time delays corresponding to (left-to-right) 1, 4, 5, 7, and 8 passes through the cavity. (b) Pulse time delay data for 8 pass (dotted) and single pass (dashed) alignment: a difference of 5.0 ns ( 152 cm) between the multiple pass and single pass signal is measured. | [
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We can carry out similar calculations for the level set
\[\varphi_{1}=x_{1}x_{2}x_{3}x_{4}-H_{1},\quad\varphi_{2}=(1-x_{1})(1-x_{2})(1-x _{3})(1-x_{4})-H_{2},\]
\[\varphi_{3}=(1-x_{2}x_{4})(1-x_{1}x_{3})-H_{3},\] (27)
and the function
\[f_{1}(\bm{x})=x_{1}{1-x_{2}+x_{2}x_{3}-x_{2}x_{3}x_{4}\over 1-x_{4}+x_{4}x_{1} -x_{4}x_{1}x_{2}}.\]
From (27) we obtain the map
\[X_{1}:=x_{1}{1-x_{2}+x_{2}x_{3}-x_{2}x_{3}x_{4}\over 1-x_{4}+x_{ 4}x_{1}-x_{4}x_{1}x_{2}}, X_{2}:=x_{2}{1-x_{3}+x_{3}x_{4}-x_{3}x_{4}x_{1}\over 1-x_{1}+x_{ 1}x_{2}-x_{1}x_{2}x_{3}},\] \[X_{3}:=x_{3}{1-x_{4}+x_{4}x_{1}-x_{4}x_{1}x_{2}\over 1-x_{2}+x_{ 2}x_{3}-x_{2}x_{3}x_{4}}, X_{4}:=x_{4}{1-x_{1}+x_{1}x_{2}-x_{1}x_{2}x_{3}\over 1-x_{3}+x_{ 3}x_{4}-x_{3}x_{4}x_{1}},\] (28)
which is known as the discrete time Painleve V. The reduction of this map yields again a biquadratic map (18) with the coefficients
\[a = (s+v-r+1)p+r-1,\] \[b = (2r-s-v-2)p-2r-s-v+2,\] \[c = (1-r)p+r+s+v-1,\] \[d = 4(1-r)p+2(r-1)(s+2)+(s+v)(4-s-v),\] \[e = (2r+s+v-2)p+(s+1)(v-2r-1)+(v-3)(v-1),\] \[f = -(r+rs+v-1)p+r+rs(r-v+1)-(v-1)^{2},\]
where \((r,s,v)=(H_{1},H_{2},H_{3})\) and \(p\) is a solution of
\[p^{2}-(r-v+1)p+r=0.\]
## III Dimensional reduction of periodicity conditions
We now study, in this section, general features of periodicity conditions and present the proof of our theorem stated in SS1.
We consider the periodicity conditions of period \(n\),
\[X_{j}^{(n)}=x_{j},\quad j=1,2,...,d.\] (29)
When the map has \(p\) invariants, the number of independent conditions of (29) is \(d-p\). Let us denote by \(\bm{\xi}=(\xi_{1},\xi_{2},...,\xi_{d-p})\) the variables which parameterize the variety \(V(h)\) of (5) after the reduction of \(p\) components of \(\bm{x}\) | [] |
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|
structure is governed by the exceptional Lie algebra \(E_{11-d}\); the gauge charges transform in a fundamental representation of this algebra, while the scalar fields parameterize a coset space \(G/H\) where \(G\) is the maximally | [
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* *Image quality: FWHM <=reff['']/20, where \(r_{\rm eff}\) is the half-light radius of the galaxy.
* *Integration time: \(t=\)S/N\(\cdot 10^{0.4\cdot(\mu_{\rm gal}-\mu_{\rm sky}+DM+\overline{M}-m_{1})}\), where \(\mu_{\rm gal}\) is the mean surface brightness of the galaxy, \(\mu_{\rm sky}\) the surface brightness of the sky background, \(DM\) the estimates distance modulus of the galaxy, \(\overline{M}\) the fluctuation luminosity of the underlying stellar population, and \(m_{1}\) the magnitude of a star providing 1 count/sec on the CCD detector at the telescope.
To give a general idea of these constraints, Fig. 1 illustrates the depth required for an image of a dE at the distance of the Fornax cluster observed with VLT+FORS1. The SBF amplitude above the shot noise level (signal-to-noise) in the power spectrum is shown as a function of integration time and mean effective surface brightness of the galaxy. A SBF distance can be determined when the S/N is approximately 0.5, (see Fig. 8 in Rekola et al. 2005), but that depends largely on the image quality i.e. seeing. For example, to achieve a S/N\(\sim\)2 in the galaxy power spectrum, the minimum exposure time required for a dE with a mean surface brightness of 25 mag arcsec\({}^{-2}\) is 1600s.
It is interesting to note that this exposure time is by a factor of 20 shorter than the 32,000s of HST time spent by Harris et al. (1998) to measure the TRGB distance of a dwarf elliptical at a similar distance.
## 3 SBF Reduction Pipeline
Previous SBF work has entailed individuals hand selecting regions in galaxy images for the analysis. To make the results as impartial as possible and data reduction more
Figure 1: An illustration how the signal-to-noise in the SBF power spectrum increases with length of exposure time and galaxy surface brightness at the distance of the Fornax Cluster. | [
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|
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### Acknowledgments
KE-F is grateful to the Theory Department at the Physics Institute of Bonn University for support. JMG-B thanks MEC, Spain, for support through a 'Ramon y Cajal' contract. LG is supported in part by NSF grant DMS-0505643 and a grant from Rutgers University Research Council. JCV acknowledges support from the Vicerrectoria de Investigacion of the University of Costa Rica.
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## 2 The model
We investigate undirected random networks with specified degree distributions1strog1 . Let \(p_{k}\) be the probability of a node having a degree k. As in previous research we will make great use of the probability generating function (PGF) corresponding to the degree distribution.
Footnote 1: The _degree_ of a node in a network is the number of connections to that node. The _degree distribution_ is a discrete probability density over the positive integers describing the probability of realizing a given degree.
Although widely employed in the probability theory and the study of stochastic branching processes, generating functions are less familiar to those working in mathematical epidemiology (but seebeck1 ; fa ; al ; an ). The utility of PGF's for the current investigation cannot be understated. Consider the degree distribution _among susceptibles_ at a given time t. As an epidemic progresses, more highly connected nodes, often called "hubs", will be preferentially culled from the population of susceptibles. Thus the degree distribution among susceptibles will evolve as the epidemic progresses. Our approach will be to keep track of the evolution of this distribution by careful application of parameters to the PGF. This will ultimately allow us to find the number of infecteds at any given time.
\begin{table} \begin{tabular}{l} \hline \({\dot{\beta}=\alpha~{}\mu~{}p_{W}}\) \\ \({\dot{\alpha}=-\alpha(r+\mu)p_{W}}\) \\ \({\dot{T}=-(r+\mu)p_{W}T-p_{W}~{}r~{}n~{}\alpha^{2}g^{\prime\prime }(\alpha+\beta)}\) \\ \({\dot{W}=p_{W}(r~{}n~{}\alpha^{2}g^{\prime\prime}(\alpha+\beta)-( r+\mu)(2W+T))}\) \\ \hline \end{tabular} \end{table} Table 1: A summary of the nonlinear differential equations used to the describe the spread of a simple SIR type epidemic through a random network. The degree distribution of the network is generated by \(g(x)\). | [
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