The classical-statistical limit of quantum mechanics

The classical-statistical limit of quantum mechanics is studied. It is proved that the limit $\hbar \to 0$ is the good limit for the operators algebra but it si not so for the state compact set. In the last case decoherence must be invoked to obtain the classical-statistical limit.Comment: 9 page

The equilibrium limit of the Casati-Prosen model

An alternative explanation of the decoherence in the Casati-Prosen model is presented. It is based on the Self Induced Decoherence formalism extended to non-integrable systems.Comment: 6 pages, no figure

On the classical limit of quantum mechanics, fundamental graininess and chaos: compatibility of chaos with the correspondence principle

The aim of this paper is to review the classical limit of Quantum Mechanics and to precise the well known threat of chaos (and fundamental graininess)to the correspondence principle. We will introduce a formalism for this classical limit that allows us to find the surfaces defined by the constants of the motion in phase space. Then in the integrable case we will find the classical trajectories, and in the non-integrable one the fact that regular initial cells become "amoeboid-like". This deformations and their consequences can be considered as a threat to the correspondence principle unless we take into account the characteristic timescales of quantum chaos. Essentially we present an analysis of the problem similar to the one of Omn\`{e}s [10,11], but with a simpler mathematical structure.Comment: 27 pages, 6 figure

The classical limit of non-integrable quantum systems

The classical limit of non-integrable quantum systems is studied. We define non-integrable quantum systems as those which have, as their classical limit, a non-integrable classical system. In order to obtain this limit, the self-induced decoherence approach and the corresponding classical limit are generalized from integrable to non-integrable systems. In this approach, the lost of information, usually conceived as the result of a coarse-graining or the trace of an environment, is produced by a particular choice of the algebra of observables and the systematic use of mean values, that project the unitary evolution onto an effective non-unitary one. The decoherence times computed with this approach coincide with those of the literature. By means of our method, we can obtain the classical limit of the quantum state of a non-integrable system, which turns out to be a set of unstable, potentially chaotic classical trajectories contained in the Wigner transformation of the quantum state.Comment: 29 page