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1.
We prove that Gibbs states for the Hamiltonian , with thes x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.  相似文献   

2.
We have calculated analytically the superheating fieldH sh for bulk superconductors, correct to second order in. We find , which agrees well with numerical computations for<0.5. The surface order parameter is , and the penetration depth is .  相似文献   

3.
Using a method developed before a set of exact solutions of the chiral equations , wheregSL(4,R) are presented.Work supported in part by CONACYT, México.  相似文献   

4.
The authors deal with the tunneling of electrons across an inhomogeneous delta-barrier defined by the potential energy (where 0$$ " align="middle" border="0"> and 0$$ " align="middle" border="0"> are two constants). In particular, the perpendicular incidence of an electron with a given value of the wave vector is considered. The electron is forward-scattered into the region behind the barrier (region 2: 0$$ " align="middle" border="0"> ), i. e. the wave function is composed of plane waves with all wave vectors such that and \left. 0 \right)} $$ " align="middle" border="0"> ) (where ). Therefore, if 0$$ " align="middle" border="0"> , the wave function of the electron is represented as , where . An approximate formula is derived for the amplitude . The authors pay a special attention to the flow density and calculate this function in two cases: 1. for the plane and 2. for high values of is the diffraction angle). The authors discuss the relevance of their diffraction problem in a prospective quantum-mechanical theory of the tunneling of electrons across a randomly inhomogeneous Schottky barrier.  相似文献   

5.
We consider the Dirichlet Laplacian for astrip in with one straight boundary and a width , where $f$ is a smooth function of acompact support with a length 2b. We show that in the criticalcase, , the operator has nobound statesfor small .On the otherhand, a weakly bound state existsprovided . In thatcase, there are positive c 1,c 2 suchthat the corresponding eigenvalue satisfies for all sufficiently small.  相似文献   

6.
This article begins with a review of the framework of fuzzy probability theory. The basic structure is given by the -effect algebra of effects (fuzzy events) and the set of probability measures on a measurable space . An observable is defined, where is the value space of X. It is noted that there exists a one-to-one correspondence between states on and elements of and between observables and -morphisms from to . Various combinations of observables are discussed. These include compositions, products, direct products, and mixtures. Fuzzy stochastic processes are introduced and an application to quantum dynamics is considered. Quantum effects are characterized from among a more general class of effects. An alternative definition of a statistical map is given and it is shown that any statistical map has a unique extension to a statistical operator. Finally, various combinations of statistical maps are discussed and their relationships to the corresponding combinations of observables are derived.  相似文献   

7.
This paper discusses certain aspects of the spectral and inverse spectral problems for the Schrödinger operator , for q(x)C(), the space of bounded continuous functions. The trace formula of the title is the relation
  相似文献   

8.
GLh(n) ×GLh(m)-covariant (hh)-bosonic[or (hh)-fermionic] algebras are built in terms of thecorresponding Rh and -matrices by contracting theGLq(n) × -covariant q-bosonic (or q-fermionic) algebras , = 1, 2.When using a basis of wherein theannihilation operators are contragredient to thecreation ones, this contraction procedure can be carried out for any n, m values. Whenemploying instead a basis wherein the annihilationoperators, like the creation ones, are irreducibletensor operators with respect to the dual quantumalgebra Uq(gl(n)) , a contraction limit only exists forn, m {1, 2, 4, 6, . . .}. For n = 2, m = 1, andn = m = 2, the resulting relations can be expressed interms of coupled (anti)commutators (as in the classical case), by usingUh(sl(2)) [instead of s1(2)] Clebsch-Gordancoefficients. Some Uh(sl(2)) rank-1/2irreducible tensor operators recently constructed byAizawa are shown to provide a realization of (2, 1).  相似文献   

9.
We consider the large time asymptotic behavior of solutions to the Cauchy problem for the modified Korteweg–de Vries equation , with initial data . We assume that the coefficient is real, bounded and slowly varying function, such that , where . We suppose that the initial data are real-valued and small enough, belonging to the weighted Sobolev space . In comparison with the previous paper (Internat. Res. Notices 8 (1999), 395–418), here we exclude the condition that the integral of the initial data u 0 is zero. We prove the time decay estimates and for all , where . We also find the asymptotics for large time of the solution in the neighborhood of the self-similar solution.  相似文献   

10.
We consider the effect of real spectral singularities on the long time behavior of the solutions of the focusing Nonlinear Schroedinger equation. We find that for each spectral singularity , such an effect is limited to the region of the (x,t)-plane in which is close to the point of stationary phase (the phase here being defined in a standard way by, say, the evolution of the Jost functions). In that region, the solution performs decaying oscillations of the same form as in the other regions, but with different parameters. The order of decay is .We prove our result by using the Riemann-Hilbert factorization formulation of the inverse scattering problem. We recover our asymptotics by transforming our problem to one which is equivalent for large time, and which can be interpreted as the one corresponding to the genus 0 algebro-geometric solution of the equation.  相似文献   

11.
Let denote the grand canonical Gibbs measure of a lattice gas in a cube of sizeL with the chemical potential and a fixed boundary condition. Let be the corresponding canonical measure defined by conditioning on . Consider the lattice gas dynamics for which each particle performs random walk with rates depending on near-by particles. The rates are chosen such that, for everyn andL fixed, is a reversible measure. Suppose that the Dobrushin-Shlosman mixing conditions holds for forall chemical potentials . We prove that for any probability densityf with respect to ; here the constant is independent ofn orL andD denotes the Dirichlet form of the dynamics. The dependence onL is optimal.Research partially supported by U.S. National Science Foundations grant 9403462, Sloan Foundation Fellowship and David and Lucile Packard Foundation Fellowship.  相似文献   

12.
Quantum uncertainties prevent simultaneous measurement of the expansion factor S(t) and its time derivative . Consequently the Hubble size has an inherent uncertainty in the quantum state that describes the semiclassical evolution of the universe. We show that the quantum uncertainty in the Hubble size of the universe is amplified to unacceptably large values in any inflationary process.This essay received an honorable mention from the Gravity Research Foundation, 1986-Ed.  相似文献   

13.
For Lax-pair isospectral deformations whose associated spectrum, for given initial data, consists of the disjoint union of a finitely denumerable discrete spectrum (solitons) and a continuous spectrum (continuum), the matrix Riemann–Hilbert problem approach is used to derive the leading-order asymptotics as of solutions to the Cauchy problem for the defocusing nonlinear Schrödinger equation ( NLSE), , with finite-density initial data
.The NLSE dark soliton position shifts in the presence of the continuum are also obtained.  相似文献   

14.
Covariant differential calculi on the quantum space for the quantum group SL q (2) are classified. Our main assumptions are thatq is not a root of unity and that the differentials de j of the generators of form a free right module basis for the first-order forms. Our result says, in particular, that apart from the two casesc =c(3), there exists a unique differential calculus with the above properties on the space which corresponds to Podles' quantum sphereS qc /2 .  相似文献   

15.
It is shown that the functional , defined onC functions on the two-dimensional sphere, satisfies the inequalityS[]0 if is subject to the constraint . The minimumS[]=0 is attained at the solutions of the Euler-Lagrange equations. The proof is based on a sharper version of Moser-Trudinger's inequality (due to Aubin) which holds under the additional constraint ; this condition can always be satisfied by exploiting the invariance ofS[] under the conformal transformations ofS 2. The result is relevant for a recently proposed formulation of a theory of random surfaces.On leave from: Istituto di Fisica dell'Università di Parma, Sezione di Fisica Teorica, Parma, Italy  相似文献   

16.
We present a complete list of all separable coordinate systems for the equations and with special emphasis on nonorthogonal coordinates. Applications to general relativity theory are indicated.  相似文献   

17.
Metallic cluster growth within a reactive polymer matrix is modeled by augmenting coagulation equations to include the influence of side reactions of metal atoms with the polymer matrix: where > 0 and where c k denotes the concentration of the kth cluster and p denotes the concentration of reactive sites available within the polymer matrix for reaction with metallic atoms. The initial conditions are required to be non-negative and satisfy and p(0) = p 0. We assume that for 01, which encompasses both bond linking kernels (R jk = j k ) and surface reaction kernels (R jk = j + k ). Our analytical and numerical results indicate that the side reactions delay gelation in some cases and inhibit gelation in others. We provide numerical evidence that gelation occurs for the classical coagulation equations ( = 0) with the bond linking kernel (d ) for 1/2<1. We examine the relative fraction of metal atoms, which coagulate compared to those which interact with the polymer matrix, and demonstrate in particular a linear dependence on –1 in the limiting case R = jk , p 0=1.  相似文献   

18.
Total electron emission from metals due to the impact of multiply charged ions, , may significantly influence quantitative measurements of ion current in corpuscular diagnostics. The value of (/q) was determined for Xe ions impacting clean polycrystalline copper as a function of ion charge state and of ion kinetic energy, keV/q, i.e. in the energy region up to keV/amu, where there is a lack of such data. For highly charged projectile ions, was found to have a clear minimum as a function of E i. With decreasing charge state of the projectile ion this minimum shifts to a lower energy and becomes shallower. This observation is in agreement with compiled results of other authors. Limits for values of are estimated and discussed.  相似文献   

19.
An analysis of the ac conductivity ac(), and the ac dielectric constant, (), of the metal-insulator percolation systems is presented in the critical regime near the transition threshold. It is argued that the polarization and relaxation of the finite fractal metallic clusters play dominant roles in controlling the dynamic response of the system on both sides of the threshold. The relaxation time constant of a fractal cluster is shown to scale with its size as withd t = 4 – 2d +d c + /, whered is tge Euclidean dimension, andd c , , and are the scaling indices for the charging, the dc conductivity, and the correlation length respectively. The average time dependent response of the system is shown to scale with a new time scale , where is the correlation length and 0 is a microscopic time constant. It is shown that at frequencies and with /dt 1, in close agreement with experiments. The effects of the anomalous transport along the infinite cluster and the medium polarizability are also discussed.  相似文献   

20.
We study Schrödinger operators of the form on d , whereA 2 is a strictly positive symmetricd×d matrix andV(x) is a continuous real function which is the Fourier transform of a bounded measure. If n are the eigenvalues ofH we show that the theta function is explicitly expressible in terms of infinite dimensional oscillatory integrals (Feynman path integrals) over the Hilbert space of closed trajectories. We use these explicit expressions to give the asymptotic behaviour of (t) for smallh in terms of classical periodic orbits, thus obtaining a trace formula for the Schrödinger operators. This then yields an asymptotic expansion of the spectrum ofH in terms of the periodic orbits of the corresponding classical mechanical system. These results extend to the physical case the recent work on Poisson and trace formulae for compact manifolds.Partially supported by the USP-Mathematisierung, University of Bielefeld (Forschungsprojekt Unendlich dimensionale Analysis)  相似文献   

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