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This paper is concerned with the study of one-body dissipation effects inidealized models resembling a nucleus. In particular, we study the quantummechanics of a free particle that collides elastically with the slowly movingwalls of a Bunimovich stadium billiard. Our results are twofold. First, wedevelop a method to solve in a simple way the quantum mechanical evolution ofplanar billiards with moving walls. The formalism is based on the {\it scalingmethod} \cite{ver} which enables the resolution of the problem in terms ofquantities defined over the boundary of the billiard. The second result isrelated to the quantum aspects of dissipation in systems with complex spectra.We conclude that in a slowly varying evolution the energy is transferred fromthe boundary to the particle through Landau$-$Zener transitions.Comment: 24 pages (including 7 postcript figures), Revtex. Submitted to PR

Characterization of Landau-Zener transitions in systems with complex spectra