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

TL;DR

This paper investigates quantum wave packet revivals in semi-classical integrable systems with two degrees of freedom, focusing on the behavior near Liouville tori using analytical methods.

Contribution

It demonstrates the phenomenon of wave packet revivals in semi-classical integrable systems with two degrees of freedom near Liouville tori, employing semi-classical analysis and number theory techniques.

Findings

Wave packet revivals are demonstrated in the studied systems.

The analysis uses semi-classical limit techniques.

Standard tools like Fourier analysis are applied.

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 phenomomenon of wave packet revivals is demonstrated in this article. The framework of this paper is semi-classical analysis (limit :). For the proofs we use standard tools of real analysis, Fourier analysis and basic analytic number theory.