Geometrical phase,generalized quasienergy and Floquet operator as invariants

TL;DR

This paper introduces generalized Floquet operators and quasienergy states as invariants in both periodic and nonperiodic quantum systems, highlighting their role in understanding geometrical phases and system dynamics.

Contribution

It extends the concept of Floquet invariants and quasienergy to nonperiodic systems with multiple characteristic times, providing new tools for analyzing quantum invariants.

Findings

Generalized Floquet operators are invariants in time-periodic systems.

Analogous invariants are identified for nonperiodic systems.

Geometrical phase is shown to be an invariant in these systems.

Abstract

For time-periodical quantum systems generalized Floquet operator is found to be integral of motion.Spectrum of this invariant is shown to be quasienergy spectrum.Analogs of invariant Floquet operators are found for nonperiodical systems with several characteristic times.Generalized quasienergy states are introduced for these systems. Geometrical phase is shown to be integral of motion.