共查询到20条相似文献,搜索用时 15 毫秒
1.
We present a rigorous computation of the dynamical entropyh of the quantum Arnold cat map. This map, which describes a flow on the noncommutative two-dimensional torus, is a simple example of a quantum dynamical system with optimal mixing properties, characterized by Lyapunov exponents ± 1n +, + > 1. We show that, for all values of the quantum deformation parameter,h coincides with the positive Lyapunov exponent of the dynamics. 相似文献
2.
Yong Moon Park 《Letters in Mathematical Physics》1994,32(1):63-74
We compute the dynamical entropy in the sense of Connes, Narnhofer, and Thirring of shift automorphism of generalized quantum Markov chains as defined by Accardi and Frigerio. For any generalized quantum Markov chain defined via a finite set of conditional density amplitudes, we show that the dynamical entropy is equal to the mean entropy.Research supported in part by the Basic Science Research Program, Korean Ministry of Education, 1993–1994. 相似文献
3.
Heide Narnhofer 《Letters in Mathematical Physics》1993,28(2):85-95
Under the assumption that there exists an optimal stationary coupling of a dynamical quantum system with a dynamical classical system, we prove that the quantum system contains an ergodic classical system. 相似文献
4.
We consider maximization of the relative entropy (with respect to a fixed normal state) in a von Neumann algebra among the states having fixed expectation for finitely many self-adjoint elements. 相似文献
5.
It is shown that with probability 1 on , resp. ongx the irrational rotation algebra
with respect to the CAT map and the generalized Price-Powers shiftA
X
are asymptotically highly anticommutative. 相似文献
6.
We construct a set of translation invariant pure states of a quantum spin chain, which is w
-dense in the set of all translation invariant states of the chain. Each of the approximating states has exponential decay of correlations, and is the unique ground state of a finite range Hamiltonian with a spectral gap above the ground state energy. 相似文献
7.
Horng-Tzer Yau 《Letters in Mathematical Physics》1991,22(1):63-80
We prove the hydrodynamic limit of Ginzburg-Landau models by considering relative entropy and its rate of change with respect to local Gibbs states. This provides a new understanding of the role played by relative entropy in the hydrodynamics of interacting particle systems.Work partially supported by U.S. National Science Foundation Grant. DMS-8806731 and Army Grant ARO-DAAL 03-88-K-0047. 相似文献
8.
We show that using the thermodynamic limit, one can give a simple and natural construction of noncommutative
spaces for quantum systems on a lattice. Within this framework, we discuss the construction and ergodicity properties of stochastic dynamics of spin flip and diffusion type. 相似文献
9.
With nary mention of a tree graph, we obtain a cluster expansion bound that includes and vastly generalizes bounds as obtained by extant tree graph inequalities. This includes applications to both two-body and many-body potential situations of the recently obtained new improved tree graph inequalities that have led to the extra 1/N! factors. We work in a formalism coupling a discrete set of boson variables, such as occurs in a lattice system in classical statistical mechanics, or in Euclidean quantum field theory. The estimates of this Letter apply to numerical factors as arising in cluster expansions, due to essentially arbitrary sequences of the basic operations: interpolation of the covariance, interpolation of the interaction, and integration by parts. This includes complicated evolutions, such as the repeated use of interpolation to decouple the same variables several times, to ensure higher connectivity for renormalization purposes, in quantum field theory.This work was supported in part by the National Science Foundation under grant no. PHY-87-01329. 相似文献
10.
11.
Reinhard Honegger 《Letters in Mathematical Physics》1993,27(3):191-203
By means of cocycle techniques in a recent paper, the global dynamics of mean field-boson couplings has been studied. Here, by restricting to the bosonic system the infinite time limit (t ) for very general initial states, one obtains time-asymptotic states on the bosonicC
*-Weyl algebra, in which one partially rediscovers the collective ordering of the infinite mean field lattice. 相似文献
12.
Peter M Alberti 《Reports on Mathematical Physics》2003,51(1):87-125
The notion of partial fidelities as invented by A. Uhlmann for pairs of finite-dimensional density matrices is extended to the νN-algebraic context and is considered and thoroughly discussed in detail from a mathematical point of view. Especially, in the case of semifinite νN-algebras, formulae and estimates for the partial fidelity between the functionals of a dense cone of inner derived normal positive linear forms are obtained. Also, some generalities on the notion of fidelity in quantum physics are collected in Appendix, and another system of mathematical axioms for fidelity over density operators, which is based on the concept of relative majorization and which is intimately related to complete positivity, is proposed. 相似文献
13.
We consider the formal non-relativistic limit (nrl) of the :?4:s+1 relativistic quantum field theory (rqft), where s is the space dimension. Following the work of R. Jackiw [R. Jackiw, in: A. Ali, P. Hoodbhoy (Eds.), Bég Memorial Volume, World Scientific, Singapore, 1991], we show that, for s = 2 and a given value of the ultraviolet cutoff κ, there are two ways to perform the nrl: (i) fixing the renormalized mass m2 equal to the bare mass ; (ii) keeping the renormalized mass fixed and different from the bare mass . In the (infinite-volume) two-particle sector the scattering amplitude tends to zero as κ → ∞ in case (i) and, in case (ii), there is a bound state, indicating that the interaction potential is attractive. As a consequence, stability of matter fails for our boson system. We discuss why both alternatives do not reproduce the low-energy behaviour of the full rqft. The singular nature of the nrl is also nicely illustrated for s = 1 by a rigorous stability/instability result of a different nature. 相似文献
14.
Orlin Stoytchev 《Letters in Mathematical Physics》1993,27(1):43-50
Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group
(the analog of the modular group) and a canonical 2 grading onA, commuting with
. We show that the functional satisfies the weak super-KMS property with respect to
and Furthermore, we prove that
and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002. 相似文献
15.
Fabio Benatti 《Letters in Mathematical Physics》1992,24(1):31-40
Two irreversible quantum evolutions with zero dynamical entropy, when dilated to reversible automorphisms, provide quantum Kolmogorov systems of both the algebraic and entropic type with infinite-dynamical entropy. 相似文献
16.
We obtain new upper bounds of critical temperatures of N-vector (Heisenberg) models. We apply a transformation of block spin type to random walk representations of the spin models, which was developed by Fröhlich et al. more than a decade ago. Though the transformation is applied just one time, the upper bounds are considerably improved. 相似文献
17.
Hideki Omori Yoshiaki Maeda Naoya Miyazaki Akira Yoshioka 《Letters in Mathematical Physics》2007,82(2-3):153-175
We propose suitable ideas for non-formal deformation quantization of Fréchet Poisson algebras. To deal with the convergence
problem of deformation quantization, we employ Fréchet algebras originally given by Gel’fand–Shilov. Ideas from deformation
quantization are applied to expressions of elements of abstract algebras, which leads to a notion of “independence of ordering
principle”. This principle is useful for the understanding of the star exponential functions and for the transcendental calculus
in non-formal deformation quantization.
Akira Yoshioka was partially supported by Grant-in-Aid for Scientific Research (#19540103.), Ministry of Education, Science
and Culture, Japan. 相似文献
18.
The Letter studies the problem of numerical approximations of the critical transition temperature and the energy gap function in the Bardeen-Cooper-Schrieffer equation arising in superconductivity theory. The positive kernel function leads to a phonon-dominant state at zero temperature. Much attention is paid to the equation defined on a bounded region. Two discretized versions of the equation are introduced. The first version approximates the desired solution from below, while the second, from above. Numerical examples are presented to illustrate the efficiency of the method. Besides, the approximations of a full space solution and the associated critical temperature by solution sequences constructed on bounded domains are also investigated.Part of this work was done while this author was visiting the Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA, 15213, USA 相似文献
19.
20.
A natural Riemannian geometry is defined on the state space of a finite quantum system by means of the Bogoliubov scalar product which is infinitesimally induced by the (nonsymmetric) relative entropy functional. The basic geometrical quantities, including sectional curvatures, are computed for a two-level quantum system. It is found that the real density matrices form a totally geodesic submanifold and the von Neumann entropy is a monotone function of the scalar curvature. Furthermore, we establish information inequalities extending the Cramér-Rao inequality of classical statistics. These are based on a very general new form of the logarithmic derivative.This work was supported by the Hungarian National Foundation for Scientific Research, grant No. 1900. Authors' e-mail addresses are: H1128PET@ella.hu and TOTH@zodiac.rutgers.edu. 相似文献