Systèmes quantiques dépendant du temps cas du spectre continu

Abstract

Since their discovery, the application of the geometric phases has been limited to the case of discrete spectra. In this work, this notion will be generalized to the case of quantum systems with continuous spectra for both adiabatic and non-adiabatic evolutions. These two results are the direct consequence of the generalization of the adiabatic theorem and the invariants theory, respectively. Among the important consequences of the obtained results, we have the demonstration of the geometrical aspect of the S matrix for any kind of time evolution. Illustrative examples are given at the end of the work.