Classical model for survival resonances close to Talbot time

TL;DR

This paper introduces a classical approximation model for survival resonances in matter wave diffraction near Talbot time, effectively replicating quantum results and enabling simpler analysis of absorption-diffraction phenomena.

Contribution

It provides the first classical model for survival resonances in matter wave diffraction, matching quantum calculations for imaginary potentials and offering analytical expressions for survival probability.

Findings

Classical model accurately reproduces quantum results for imaginary potentials.

Model simplifies evolution of phase-space densities in absorption-diffraction.

Analytical expression for survival probability derived in the classical limit.

Abstract

We present a classical approximation for the peaks of survival resonances occurring when diffracting matter waves from absorption potentials. Generally our simplified model describes the absorption-diffraction process around the Talbot time very well. Classical treatments of this process are presently lacking. For purely imaginary potentials, the classical model duplicates quantum mechanical calculations. The classical model allows for simple evolution of phase-space probability densities, which in the limit of the effective Planck's constant going to zero allows for a compact analytical expression of the survival probability as a function of remaining parameters. Our work extends the range of processes that can be described through classical analogues.