Quantum revivals in two degrees of freedom integrable systems: The torus case

Article type: Research Article

Authors: Lablée, Olivier

Affiliations: Université Grenoble 1-CNRS, Institut Fourier, UFR de Mathématiques, UMR 5582, BP 74 38402 Saint Martin d'Hères Cedex, France. E-mail: lablee@ujf-grenoble.fr

Abstract: The paper deals with the semi-classical behaviour of quantum dynamics for a semi-classical completely integrable system with two degrees of freedom near Liouville regular torus. The phenomenon of wave packet revivals is demonstrated in this article. The framework of this paper is semi-classical analysis (limit: h→0). For the proofs we use standard tools of real analysis, Fourier analysis and basic analytic number theory.

Keywords: Schrödinger's dynamics, revivals of wave packets, semi-classical analysis of two degrees of freedom integrable systems

DOI: 10.3233/ASY-2011-1069

Journal: Asymptotic Analysis, vol. 77, no. 1-2, pp. 1-41, 2012