Asymptotic Scattering by Poissonian Thermostats

TL;DR

This paper analyzes how an infinite chain of harmonic oscillators with a Poisson thermostat scatters wave energy, revealing unique scattering behavior and wave frequency changes in the macroscopic limit.

Contribution

It provides the first detailed analysis of wave scattering by a Poisson thermostat, contrasting it with Langevin thermostats and showing the generation of new wave frequencies.

Findings

Derived reflection, transmission, and scattering coefficients at high frequencies.

Discovered that Poissonian thermostats produce a continuous wave cloud with different frequencies.

Contrasted Poissonian thermostat scattering with Langevin thermostat behavior.

Abstract

We consider an infinite chain of coupled harmonic oscillators with a Poisson thermostat at the origin. In the high frequency limit, we establish the reflection-transmission-scattering coefficients for the wave energy scattered off the thermostat. Unlike the case of the Langevin thermostat [5], in the macroscopic limit the Poissonian thermostat scattering generates a continuous cloud of waves of frequencies different from that of the incident wave.