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 Time-Asymmetry and the Entropy Gap

The universe time-asymmetry is essentially produced by its low-entropy unstable initial state. Using quanlitative arguments, Paul Davies has demonstrated that the universe expansion may diminish the entropy gap, therefore explaining its low-entropy state, with respect to the maximal possible entropy at any time. This idea is implemented in a qualitative way\thinspace in a simple homogeneous model. Some rough coincidence with observational data are foundComment: 5 page