Almost Periodic Orbits and Stability for Quantum Time-Dependent Hamiltonians

TL;DR

This paper investigates the conditions under which quantum systems with time-dependent Hamiltonians exhibit almost periodic orbits and discusses stability criteria, providing theoretical insights and specific examples for different types of time dependence.

Contribution

It establishes a characterization of almost periodic orbits for periodic Hamiltonians and presents an example of precompact but not almost periodic orbits in quasiperiodic cases.

Findings

Almost periodic orbits are equivalent to precompactness in periodic systems.

Precompact but not almost periodic orbits exist in quasiperiodic systems.

Simple conditions for dynamical stability in nonautonomous quantum systems are discussed.

Abstract

We study almost periodic orbits of quantum systems and prove that for periodic time-dependent Hamiltonians an orbit is almost periodic if, and only if, it is precompact. In the case of quasiperiodic time-dependence we present an example of a precompact orbit that is not almost periodic. Finally we discuss some simple conditions assuring dynamical stability for nonautonomous quantum system.