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Models of quantum and classical particles on the d-dimensional cubic lattice with pair interparticle interactions are considered. The classical model is obtained from the corresponding quantum one when the reduced physical mass of the particle tends to infinity. For these models, it is proposed to define the convergence of the Euclidean Gibbs states, when the reduced mass tends to infinity, by the weak convergence of the corresponding Gibbs specifications, determined by conditional Gibbs measures. In fact it is proved that all conditional Gibbs measures of the quantum model weakly converge to the conditional Gibbs measures of the classical model. A similar convergence of the periodic Gibbs measures and, as a result, of the order parameters, for such models with the pair interactions possessing the translation invariance, has also been proven.
The embedding of a manifold M into a Hilbert-space H induces, via the pull-back, a tensor field on M out of the Hermitian tensor on H. We propose a general procedure to compute these tensors in particular for manifolds admitting a Lie-group structure.
In this article we discuss our ongoing program to extend the scope of certain, well-developed microlocal methods for the asymptotic solution of Schr{o}dingers equation (for suitable `nonlinear oscillatory quantum mechanical systems) to the treatment
We deal with the reversible dynamics of coupled quantum and classical systems. Based on a recent proposal by the authors, we exploit the theory of hybrid quantum-classical wavefunctions to devise a closure model for the coupled dynamics in which both
This paper presents the momentum map structures which emerge in the dynamics of mixed states. Both quantum and classical mechanics are shown to possess analogous momentum map pairs. In the quantum setting, the right leg of the pair identifies the Ber
We review some recent developments in the study of Gibbs and non-Gibbs properties of transformed n-vector lattice and mean-field models under various transformations. Also, some new results for the loss and recovery of the Gibbs property of planar ro