Trace formulas for time periodic complex Hamiltonians on lattice

TL;DR

This paper derives trace formulas for time-periodic complex Hamiltonians on lattices and uses them to estimate eigenvalues of the quasienergy operator based on potential norms.

Contribution

It introduces trace formulas for complex, time-periodic lattice Hamiltonians and links eigenvalue estimates to potential norms, advancing spectral analysis methods.

Findings

Derived explicit trace formulas for complex Hamiltonians on lattices.

Established eigenvalue bounds for the quasienergy operator.

Connected spectral properties to potential norms.

Abstract

We consider time periodic Hamiltonians with complex potentials on the lattice and determine trace formulas. As a corollary we estimate eigenvalues of the quasienergy operator in terms of the norm of potentials.