Characterization of Landau-Zener transitions in systems with complex spectra

M.J. SÁNCHEZ, E. VERGINI AND D. WISNIACKI

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Año: 1996 vol. 54 p. 4812 - 4818

1539-3755

This paper is concerned with the study of one-body dissipation effects in idealized models resembling a nucleus. In particular, we study the quantum mechanics of a free particle that collides elastically with the slowly moving walls of a Bunimovich stadium billiard. Our results are twofold. First, we develop a method to solve in a simple way the quantum mechanical evolution of planar billiards with moving walls. The formalism is based on the scaling method [E. Vergini and M. Saraceno, Phys. Rev. E 52, 2204 (1995)] which enables the resolution of the problem in terms of quantities defined over the boundary of the billiard. The second result is related to the quantum aspects of dissipation in systems with complex spectra. We conclude that in a slowly varying evolution the energy is transferred from the boundary to the particle through Landau-Zener transitions.