共查询到20条相似文献,搜索用时 62 毫秒
1.
We consider the ground-state of the quantum spin model
in one-dimension, where {h
i, iZ} are independent identically distributed random variables. By means of a Jordan-Wigner transformation the model is mapped into a free Fermi gas in the presence of a random external potential. We then use exponential localization of the one particle states to prove exponential decay for the spin-spin correlation functions.Partially supported by the NSF under grants DMS8702301 and INT8703059Partially supported by the CNPq under grant 303795-77FA 相似文献
2.
Large Deviations for Quantum Spin Systems 总被引:1,自引:0,他引:1
We consider high temperature KMS states for quantum spin systems on a lattice. We prove a large deviation principle for the distribution of empirical averages
, where the X
i
's are copies of a self-adjoint element X (level one large deviations). From the analyticity of the generating function, we obtain the central limit theorem. We generalize to a level two large deviation principle for the distribution of
相似文献
3.
Przemysław Górka 《Letters in Mathematical Physics》2007,79(2):193-201
In this paper we deal with the following equation: on a three-dimensional Riemannian manifold . We assume that the volume of Σ, the norm , and are small enough. Using a rather simple argument we show the existence of solution to the problem.
Dedicated to Gosia and Basia. 相似文献
4.
Haluk Beker 《Foundations of Physics》1998,28(6):999-1004
A purely algebraic perturbation theory based on deforming the generators of the dynamical group SU(1, 1) is applied to the l = 0 Morse potential problem with
. In particular, perturbations of the form
and
are treated explicitly. 相似文献
5.
On the Schrödinger equation and the eigenvalue problem 总被引:1,自引:0,他引:1
If
k
is thek
th eigenvalue for the Dirichlet boundary problem on a bounded domain in
n
, H. Weyl's asymptotic formula asserts that
, hence
. We prove that for any domain and for all
. A simple proof for the upper bound of the number of eigenvalues less than or equal to - for the operator –V(x) defined on
n
(n3) in terms of
is also provided.Research partially supported by a Sloan Fellowship and NSF Grant No. 81-07911-A1 相似文献
6.
A. H. Völkel 《Communications in Mathematical Physics》1966,2(1):176-214
By subtraction of products of three-point functions the four-point functions in relativistic quantum field theory are decomposed into two parts, in one of which there does not occur any mass-shell-singularity in the variables (; 1, 4). All these singularities are given explicitly by the kernels of the products of the three-point functions. — Necessary and sufficient conditions for the non-triviality of unitaryS-matrices or some of their elements are proved in terms of statements on the occurence of mass-shell-singularities in the vacuum expectation values of field operators. The strongest result we have gained is: If
is equal to zero for someN>3, then all transition amplitudesT
2n
vanish for everyn. 相似文献
7.
Let
be the Haag--Kastler net generated by the
(2) chiral current algebra at level 1. We classify the SL(2,
)-covariant subsystems
by showing that they are all fixed points nets
H
for some subgroup H of the gauge automorphisms group SO(3) of
. Then, using the fact that the net
1 generated by the
(1) chiral current can be regarded as a subsystem of
, we classify the subsystems of
1. In this case, there are two distinct proper subsystems: the one generated by the energy-momentum tensor and the gauge invariant subsystem
. 相似文献
8.
Hirokazu Nishimura 《International Journal of Theoretical Physics》1994,33(6):1173-1188
Any manual
of Boolean locales in the strong sense, namely a subcategory of the opposite category
of the category
of complete Boolean algebras and complete Boolean homomorphisms satisfying not only conditions (3.1)–(3.10) of our previous paper [International Journal of Theoretical Physics,32, 1293 (1993b)], but also conditions (4.1)–(4.4) of that paper, is shown to be representable as the second-class orthomodular manual
of Boolean locales on an orthomodular poset
In this sense the study on manuals of Boolean locales in the strong sense is tantamount to the study on a special class of orthomodular posets, though our viewpoint is radically different from the conventional one in the traditional approach to orthomodular posets. Then the notion of a manual of Hilbert spaces or exactly what is called a manual of Hilbert locales is introduced, over which a variant of the celebrated Gelfand-Naimark-Segal theorem for a manual of Boolean locales in the strong sense is established. 相似文献
9.
We use the real-space renormalization group method to study the critical behavior of self-avoiding walks (SAWs) on both site percolation clusters at percolation threshold and site lattice animals in a square lattice. The correlation length exponents of SAWs are found to be
on the percolation clusters atp
c
and
SAW
LA
=0.804 on lattice animals. These results are compared with Kremer's suggestion of modified Flory formula
where
is the fractal dimension of the fractal object. 相似文献
10.
The fusion rules for the (p,q)-minimal model representations of the Virasoro algebra are shown to come from the group
in the following manner. There is a partition
into disjoint subsets and a bijection between
and the sectors
of the (p,q)-minimal model such that the fusion rules
correspond to
where
. 相似文献
11.
A general class of Lorentzian metrics,
,
, with
any Riemannian manifold, is introduced in order to generalize classical exact plane fronted waves. Here, we start a systematic study of their main geodesic properties: geodesic completeness, geodesic connectedness and multiplicity causal character of connecting geodesics. These results are independent of the possibility of a full integration of geodesic equations. Variational and geometrical techniques are applied systematically. In particular, we prove that the asymptotic behavior of H(x,u) with x at infinity determines many properties of geodesics. Essentially, a subquadratic growth of H ensures geodesic completeness and connectedness, while the critical situation appears when H(x,u) behaves in some direction as
, as in the classical model of exact gravitational waves. 相似文献
12.
We consider the double-scaling limit in the hermitian matrix model for 2D quantum gravity associated with the measure exp
. We show that after the appropriate modification of the contour of integration the Cross-Migdal-Douglas-Shenker limit to the Painlevé I equation (in the generic case of the pure gravity) is valid and calculate the nonperturbative parameters of the corresponding Painlevé function. Our approach is based on the WKB-analysis of the L-A pair corresponding to the discrete string equation in the framework of the Inverse Monodromy Method. Here we extend our results, which were obtained before for the particular casesN=2,3. Our analysis complements the isomonodromy approach proposed by G. Moore to the general string equations that come from the matrix model in the continuous limit and differ in that we apply the isomonodromy technique to investigate the double scaling limit itself. 相似文献
13.
We consider the time-dependent Schrödinger-Hartree equation (1) $$iu_t + \Delta u = \left( {\frac{1}{r}*|u|^2 } \right)u + \lambda \frac{u}{r},(t, x) \in \mathbb{R} \times \mathbb{R}^3 ,$$ (2) $$u(0,x) = \phi (x) \in \Sigma ^{2,2} ,x \in \mathbb{R}^3 ,$$ where λ≧0 and \(\Sigma ^{2,2} = \{ g \in L^2 ;\parallel g\parallel _{\Sigma ^{2,2} }^2 = \sum\limits_{|a| \leqq 2} {\parallel D^a g\parallel _2^2 + \sum\limits_{|\beta | \leqq 2} {\parallel x^\beta g\parallel _2^2< \infty } } \} \) . We show that there exists a unique global solutionu of (1) and (2) such that $$u \in C(\mathbb{R};H^{1,2} ) \cap L^\infty (\mathbb{R};H^{2,2} ) \cap L_{loc}^\infty (\mathbb{R};\Sigma ^{2,2} )$$ with $$u \in L^\infty (\mathbb{R};L^2 ).$$ Furthermore, we show thatu has the following estimates: $$\parallel u(t)\parallel _{2,2} \leqq C,a.c. t \in \mathbb{R},$$ and $$\parallel u(t)\parallel _\infty \leqq C(1 + |t|)^{ - 1/2} ,a.e. t \in \mathbb{R}.$$ 相似文献
14.
Marcus Pivato 《Journal of statistical physics》2003,110(1-2):247-267
If
, and
is a finite (nonabelian) group, then
is a compact group; a multiplicative cellular automaton (MCA) is a continuous transformation
which commutes with all shift maps, and where nearby coordinates are combined using the multiplication operation of
. We characterize when MCA are group endomorphisms of
, and show that MCA on
inherit a natural structure theory from the structure of
. We apply this structure theory to compute the measurable entropy of MCA, and to study convergence of initial measures to Haar measure. 相似文献
15.
Recently, new rigorous results concerning integrals of exact memory functions in the time-convolution Generalized Master Equations (GME) for state occupation probabilities, governing relaxation of open quantum systems, have been obtained. They include that a) time integrals of exact memories
and b) memories w
ij(t) have tails unobtainable by perturbational arguments which cause that
does not exist or is infinite. For a two-level system, a simple model for such memories is considered and solved. It is concluded that GME may yield that with increasing time, the system unphysically more and more deviates from equilibrium, indicating thus instability of the equilibrium distribution. Thus, in contrast to, e.g., the famous Boltzmann equation, the mathematical structure of GME alone does not guarantee the stability of the equilibrium state. 相似文献
16.
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
17.
C. P. Boyer E. G. Kalnins Willard Miller Jr. 《Communications in Mathematical Physics》1978,59(3):285-302
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
18.
G. Andrei Mezincescu Daniel Bessis Jean-Daniel Fournier Giorgio Mantica Francisc D. Aaron 《Journal of statistical physics》1997,86(3-4):675-705
The average density of zeros for monic generalized polynomials,
, with real holomorphic ,f
k
and real Gaussian coefficients is expressed in terms of correlation functions of the values of the polynomial and its derivative. We obtain compact expressions for both the regular component (generated by the complex roots) and the singular one (real roots) of the average density of roots. The density of the regular component goes to zero in the vicinity of the real axis like |lmz|. We present the low- and high-disorder asymptotic behaviors. Then we particularize to the large-n limit of the average density of complex roots of monic algebraic polynomials of the form
with real independent, identically distributed Gaussian coefficients having zero mean and dispersion
. The average density tends to a simple,universal function of =2nlog|z| and in the domain coth(/2)n|sin arg(z)|, where nearly all the roots are located for largen. 相似文献
19.
Models of random systems whose Hamiltonian reads
, where
and
i
,=1,...,n are independent, identically distributed random variables are discussed.J
ij
are assumed to be symmetric, with respect toJ
0, random variables and also symmetric functions of components of
. A question of dependence of a phase diagram on a probability distribution of
is addressed. A class of distributions and interactionsJ
ij
, which give rise to phase diagrams called typical is selected. Then a problem of obtaining typical phase diagrams, containing a certain region with an infinite number of pure phases, is studied. 相似文献
20.
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