Pure point spectrum for the time evolution of a periodically rank-N kicked Hamiltonian

TL;DR

This paper establishes conditions for the spectrum of periodically rank-N kicked quantum systems to be pure point, aiding the analysis of quantum stability and chaos in such systems.

Contribution

It extends previous rank-1 results to rank-N systems, providing new theorems for spectral stability in periodically kicked quantum systems.

Findings

Spectrum remains pure point under certain conditions.

Extends stability results from rank-1 to rank-N systems.

Provides unitary theorems analogous to self-adjoint theory.

Abstract

We find the conditions under which the spectrum of the unitary time evolution operator for a periodically rank-N kicked system remains pure point. This stability result allows one to analyse the onset of, or lack of chaos in this class of quantum mechanical systems, extending the results for rank-1 systems produced by Combescure and others. This work includes a number of unitary theorems equivalent to those well known and used in the self-adjoint theory.