The number of eigenvalues of discrete Hamiltonian periodic in time

TL;DR

This paper investigates the spectral properties of time-periodic Hamiltonians on periodic graphs, providing estimates for the number of quasi-energy eigenvalues within a finite interval.

Contribution

It offers new bounds on the count of eigenvalues for discrete Hamiltonians with time-periodic structure on graphs.

Findings

Derived estimates for eigenvalue counts within finite intervals.

Extended spectral analysis to time-periodic Hamiltonians on graphs.

Provided theoretical bounds applicable to quantum graph models.

Abstract

We consider time periodic Hamiltonian on periodic graphs and estimate the number of its quasi-energy eigenvalues on the finite interval.