Non-integrability and mixing in quantum systems: on the way to quantum chaos

MARIO CASTAGNINO; OLIMPIA LOMBARDI

STUDIES IN HISTORY AND PHILOSOPHY OF SCIENCE

ELSEVIER SCI LTD

Año: 2007 vol. 38 p. 482 - 513

0039-3681

In spite of the increasing attention that quantum chaos has received from physicists in recent times, when the subject is considered from a conceptual viewpoint the usual opinion is that there is some kind of conflict between quantum mechanics and chaos. In this paper we follow the program of Belot and Earman, who propose to analyze the problem of quantum chaos as a particular case of the classical limit of quantum mechanics. In particular, we address the problem on the basis of our account of the classical limit, which in turn is grounded on the self-induced approach to decoherence. This strategy allows us to identify the conditions that a quantum system must satisfy to lead to nonintegrability and to mixing in the classical limit.