Exponential decay and resonances in a driven system

TL;DR

This paper investigates resonance phenomena in a periodically driven quantum system, employing Floquet theory and building on previous work to characterize resonances via survival probability behavior.

Contribution

It introduces a novel approach combining Floquet-Howland formalism with existing resonance results to analyze time-dependent Hamiltonian perturbations.

Findings

Resonances are characterized through the time evolution of survival probability.

The approach extends resonance analysis to time-periodic Hamiltonians.

The method integrates Floquet theory with prior resonance results.

Abstract

We study the resonance phenomena for time periodic perturbations of a Hamiltonian $H$ on the Hilbert space $L^2(\mathbb R ^d)$. Here, resonances are characterized in terms of time behavior of the survival probability. Our approach uses the Floquet-Howland formalism combined with the results of L. Cattaneo, J.M. Graf and W. Hunziker on resonances for time independent perturbations.