Asymptotic Scattering by Poissonian Thermostats

In the present paper, we consider an infinite chain of harmonic oscillators coupled with a Poisson thermostat attached at a point. The kinetic limit for the energy density of the chain, given by the Wigner distribution, satisfies a transport equation outside the thermostat location. A boundary condition emerges at this site, which describes the reflection-transmission-scattering of the wave energy scattered off by the thermostat. Formulas for the respective coefficients are obtained. Unlike the case of the Langevin thermostat studied in Komorowski et al. (Arch. Ration. Mech. Anal. 237, 497-543, 2020), the Poissonian thermostat scattering generates in the limit a continuous cloud of waves of frequencies different from that of the incident wave.

Automated summary

In this paper, an infinite chain of harmonic oscillators coupled with a Poisson thermostat is investigated. The energy density of the chain, described by the Wigner distribution, satisfies a transport equation outside the location of the thermostat. A boundary condition arises at this site, which explains the reflection-transmission-scattering of the wave energy influenced by the thermostat. The coefficients for these processes are obtained. Unlike the Langevin thermostat case studied in Komorowski et al. (Arch. Ration. Mech. Anal. 237, 497-543, 2020), the Poissonian thermostat scattering generates a continuous cloud of waves with frequencies different from the incident wave in the limit.