High frequency limit for a chain of harmonic oscillators with a point Langevin thermostat

TL;DR

This paper analyzes how wave energy scatters in an infinite chain of harmonic oscillators with a localized Langevin thermostat, revealing that high-frequency scattering remains uncoupled despite time-dependent fluctuations.

Contribution

It establishes the reflection and transmission coefficients for wave energy in the high-frequency limit of a harmonic oscillator chain with a point thermostat, showing frequency decoupling.

Findings

Reflection and transmission coefficients are derived for high-frequency scattering.

Wave energy at different frequencies remains uncoupled despite thermostat fluctuations.

The thermostat's time-dependent fluctuations do not affect frequency coupling in scattering.

Abstract

We consider an infinite chain of coupled harmonic oscillators with a Langevin thermostat at the origin. In the high frequency limit, we establish the reflection-transmission coefficients for the wave energy for the scattering of the thermostat. To our surprise, even though the thermostat fluctuations are time-dependent, the scattering does not couple wave energy at various frequencies.