Quantum Energy Expectation in Periodic Time-Dependent hamiltonians via Green Functions

TL;DR

This paper derives a formula linking the Laplace time average of a probe energy's expectation value in a periodic time-dependent Hamiltonian to eigenvalues and Green functions, aiding analysis of quantum energy expectations.

Contribution

It introduces a novel formula connecting time-averaged energy expectations with Green functions for periodic Hamiltonians, enhancing analytical tools in quantum dynamics.

Findings

The formula effectively relates energy expectation averages to spectral data.

Applications demonstrate the formula's practical usefulness.

Supports analysis of quantum systems with time-periodic Hamiltonians.

Abstract

Let $U_F$ be the Floquet operator of a time periodic hamiltonian $H(t)$. For each positive and discrete observable $A$ (which we call a {\em probe energy}), we derive a formula for the Laplace time average of its expectation value up to time $T$ in terms of its eigenvalues and Green functions at the circle of radius $e^{1/T}$. Some simple applications are provided which support its usefulness.