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1.
On orthogonal and symplectic matrix ensembles 总被引:1,自引:0,他引:1
The focus of this paper is on the probability,E
(O;J), that a setJ consisting of a finite union of intervals contains no eigenvalues for the finiteN Gaussian Orthogonal (=1) and Gaussian Symplectic (=4) Ensembles and their respective scaling limits both in the bulk and at the edge of the spectrum. We show how these probabilities can be expressed in terms of quantities arising in the corresponding unitary (=2) ensembles. Our most explicit new results concern the distribution of the largest eigenvalue in each of these ensembles. In the edge scaling limit we show that these largest eigenvalue distributions are given in terms of a particular Painlevé II function. 相似文献
2.
For an Ising ferromagnet with nearest-neighbour interactions of strengthK and surface magnetic fieldh, the surface free energy in the presence of a positively (or negatively) magnetized zero-field bulk phase is shown to be analytic inh for Reh<K–/, where =2.96 ... and is the inverse temperature. This puts the lower boundK–/ on the values ofh at which wetting and layering transitions can take place. 相似文献
3.
We consider some models of classical statistical mechanics which admit an investigation by means of the theory of dominant ground states. Our models are related to the Gibbs ensemble for the multidimensional SOS model with symmetric constraints
x
m/2. The main result is that for 0, where 0 does not depend onm, the structure of thermodynamic phases in the model is determined by dominant ground states: for an evenm a Gibbs state is unique and for an oddm the number of space-periodic pure Gibbs states is two. 相似文献
4.
Ricardo S. Schor 《Communications in Mathematical Physics》1984,92(3):369-395
We study the mass spectrum up to –7 (1–) log of pure three-dimensional lattice gauge theories with action
(g
P) for real irreducible and small . Besides the lowest excitationm
0–4log, we find two nearly degenerate excited statesm
1,m
2 withm
i–6log (i=1, 2) and (m
1–m
2) at leastO().Work partially supported by CNPq (Brasil) 相似文献
5.
R. P. Wallner 《General Relativity and Gravitation》1980,12(9):719-732
Some of the proposed Lagrangians and their corresponding field equations for a gravitational theory based on a Riemann-Cartan space with metric-compatible connection (U
4, theory) are compared and a new one is suggested. This Lagiangian, and that of P. von der Heyde and F. W. Hehl et al. are examined applying the Gordon-decomposition argument. Finally, Einstein's field equations with cosmological term are shown to be included in some sense, but the cosmological constant naturally has microphysical origin. To simplify notation, Cartan's calculus is used throughout.Work supported by Fonds zur Förderung der wissenschaftlichen Forschung in österreich, project No. 3666.Most of this work was carried out during the stay at the 6th Course of the International School of Cosmology and Gravitation at Erice, 1979. 相似文献
6.
M. I. Faingol'd 《Russian Physics Journal》1987,30(4):291-294
The coherent scattering of spin-S particles by a monatomic crystal film is considered, with rescattering taken into account. A relation between the amplitudes qj of different diffraction orders and the dielectric tensor
() of the two-dimensional crystal is found. The relation can be used to obtain
() for an arbitrary frequency (including resonant frequencies) in terms of elastic scattering data. The possibility of bound states of the particles in the monatomic film is demonstrated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 30–34, April, 1987.The author thanks V. L. Vinetskii for interest in the work and for useful discussions. 相似文献
7.
We analyze the low-temperature phase of ferromagnetic Kax-Ising models in dimensionsd2. We show that if the range of interactions is –1, then two disjoint translation-invariant Gibbs states exist if the inverse temperature satisfies –1N, where =d(1–)/(2d+2)(d+1), for any >0. The proof involves the blocking procedure usual for Kac models and also a contour representation for the resulting long-range (almost) continuous-spin system which is suitable for the use of a variant of the Peierls argument. 相似文献
8.
Joseph G. Conlon 《Journal of statistical physics》1990,58(1-2):265-293
A classical gas with short-range interaction in the grand canonical ensemble is studied. Ifp(, z) denotes the thermodynamic pressure at inverse temperature and activityz, then it follows from the Mayer expansion thatp(, z) is infinitely differentiable provided andz are sufficiently small. Here it is shown that there exists
0>0 such thatp(, z) is infinitely differentiable if<
0 andz>0. One can interpret this result as saying that (
0)–1 is an upper bound on the critical temperature for the system. 相似文献
9.
We study the antiferromagnetic q-state Potts model on the square lattice for q=3 and q=4, using the Wang–Swendsen–Kotecký (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q=3 we obtain good control up to correlation length 5000; the data are consistent with ()=Ae
2
p
(1+a
1
e
–
+ ...) as , with p1. The staggered susceptibility behaves as
stagg
5/3. For q=4 the model is disordered (2) even at zero temperature. In appendices we prove a correlation inequality for Potts antiferromagnets on a bipartite lattice, and we prove ergodicity of the WSK algorithm at zero temperature for Potts antiferromagnets on a bipartite lattice. 相似文献
10.
Mitsunobu Miyagi 《Optical and Quantum Electronics》1989,21(1):63-67
It is shown theoretically that the field shift x and phase constant change in two-dimensional three-layered dielectric or hollow waveguides bent uniformly with large bending radiusR are related by x = 2R/
0, where
0 is the axial phase constant. The relationship predicts that the field distributions of the TE0 or TM0 mode shift toward the outward direction of bending, whereas those of other TE
n
or TM
n
(n=1,2,...) modes shift inward in a hollow waveguide. Characteristic features in dielectric waveguides are also described. 相似文献
11.
Alain Joye 《Journal of statistical physics》1994,75(5-6):929-952
The spectrum of the Floquet operator associated with time-periodic perturbations of discrete Hamiltonians is considered. If the gap between successive eigenvalues
j
of the unperturbed Hamiltonian grows as
j
-
j-1
j
and the multiplicity of
j
grows asj
with >0 asj tends to infinity, then the corresponding Floquet operator possesses no absolutely continuous spectrum provided the perturbation is smooth enough. 相似文献
12.
André Gleyzal 《Foundations of Physics》1976,6(3):299-303
An analytic gravitational fieldZ
(Z
y
) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds
2
=zdzdz of four complex variables z=t, x, y, x the field equationsR
Rz
= –(U
U
– Z
) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if =(Z
v) and =(z
) are expressed in terms of the conventional mass density function
, the conventional charge density function
, and a pressurep as follows:
v=const=p/c
2–10–29 gm/cm3. 相似文献
13.
James F. Woodward 《Foundations of Physics》1982,12(5):467-478
The Faradayan hypothesis of inductive coupling of the electromagnetic and gravitational fields is briefly discussed. An experiment designed to test the hypothesis wherein samples are spun to see if any electrogravitational charge is induced is described. Results of the experiment are reported. They imply the induction of a charge density * for spinning samples that behaves as *=ma, where m is the mass density of an element of matter experiencing an acceleration a, and is the coupling coefficient for the hypothetical electrogravitational induction effect. In this experiment, is found to have the value(9.6±3.3)×10
–13
statcoulombs/dyne. Tests that seem to rule out explanations of the observed charges in terms of conventional charging mechanisms are considered. 相似文献
14.
Ganeev R. A. Ryasnyansky A. I. Tugushev R. I. Kodirov M.K. Akhmedjanov F. R. Usmanov T. 《Optical and Quantum Electronics》2004,36(9):807-818
Nonlinear refraction, nonlinear absorption and optical limiting in photorefractive crystals Bi12SiO20(BSO) and Bi12GeO20(BGO) at the wavelengths of 1064 and 532 nm were investigated. It was shown that both BSO and BGO crystals possess by positive nonlinear refraction in two investigated spectral ranges (n
2
BSO=(2.5 ± 0.5)× 10–12 esu, n
2
BGO=(6.3 ± 1.3)× 10–12 esu at equals 1064 nm; n
2
BSO=(4.4 plusmn; 0.9)× 10–12 esu, n
2
BGO=(7.4 ± 1.5)× 10–12 esu at = 532 nm). The nonlinear absorption was due to three-photon absorption at the wavelength of 1064 nm (
(3)
BSO=(2.5 ± 0.8)× 10–20cm3W–2,
(3)
BSO=(4.4 ± 1.3)× 10–20cm3W–2) and two-photon absorption at the wavelength of 532 nm (
(2)
BSO=(2 ± 0.4)× 10–9cm W–1,
(2)
BGO=(3.7 ± 0.7)× 10–9cm W–1). 相似文献
15.
The gyroscope in an orbiting satellite will be acted on by additional gravitational fields due to the rotation of the earth and due to the orbital velocity of the satellite. According to special relativistic gravitational theory, we deduce
L
(S)
—the gyroscope's precession rate due to the orbital velocity—and
S
(S)
—the gyroscope's precession rate due to the earth's rotation in the polar orbit case. The results are
L
(S)
= (2/3)
L
(G)
,
S
(S)
= (3/2) cos (1 - sin2 cos2)1/2
S
(G)
, where and are the gyroscope's polar angles, and
L
(G)
and
S
(G)
are the geodetic and frame-dragging precession rates predicted by general relativity, respectively. 相似文献
16.
Nobuo Yoshida 《Journal of statistical physics》1998,90(3-4):1015-1035
We consider Glauber dynamics on a finite cube in d-dimensional lattice (d2), which is associated with basic Ising model at temperature T=1/1 under a magnetic field h > 0. We prove that if the effective magnetic field is positive, then the relaxation of the Glauber dynamics in the uniform norm is exponentially fast, uniformly over the size of underlying cube. The result covers the case of the free-boundary condition with arbitrarily small positive magnetic field. This paper is a continuation of an attempt initiated earlier by Schonmann and Yoshida to shed more light on the relaxation of the finite-volume Glauber dynamics when the thermodynamic parameter (, h) is so near the phase transition line, (, h);
c
< &h = 0, that the Dobrushin–Shlosman mixing condition is no longer available. 相似文献
17.
Charles Radin 《Communications in Mathematical Physics》1971,23(3):189-198
By introducing a specific type of perturbation,A, in the Hamiltonian, we define a class of gently perturbed states, ,A, of a canonical ensemble, . The perturbations are chosen so as to preserve a relationship of the form ,A constant ×. Applications in ergodic theory and phase transitions are described. 相似文献
18.
P. Vieillefosse 《Journal of statistical physics》1994,74(5-6):1195-1209
The Coulomb pair density matrixG
(r, r) for attractive and repulsive potentials is not only interesting for determining the two-particle effective potentials, but it is also essential in numerical studies of quantum systems. A high-temperature approximation is obtained for logG
(r, r), in the form of simple integrals or series expansions; large-distance expansions are also given. 相似文献
19.
Theoretical and experimental aspects of the study of the e-- problem in effects of neutral weak currents in colliding e+e– beams in the region of the Z resonance are discussed. Quantities that describe the degree of violation of e-- universality are analyzed. In particular, it is shown that by measuring the spin asymmetry for angles 160° it is possible to determine the degree of violation ofl-e universality =g
A
e
g
V
l
–g
V
e
g
A
l
to an accuracy of up to 0.01.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 88-91, May, 1989. 相似文献
20.
Critical temperature of the classical O(N) spin model in two dimensions is investigated. We show that no phase transition exists in the system if the inverse temperature is less than c=c(N), where c(N) is a constant such that c(N) > const. N log N. 相似文献