High Frequency Limit for a Chain of Harmonic Oscillators with a Point Langevin Thermostat

Tomasz Komorowski; Stefano Olla; Lenya Ryzhik; Herbert Spohn

doi:10.1007/s00205-020-01513-7

High Frequency Limit for a Chain of Harmonic Oscillators with a Point Langevin Thermostat

Tomasz Komorowski, Stefano Olla, Lenya Ryzhik, Herbert Spohn

TUM Emeriti of Excellence

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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 off the thermostat. To our surprise, even though the thermostat fluctuations are time-dependent, the scattering does not couple wave energy at various frequencies.

Original language	English
Pages (from-to)	497-543
Number of pages	47
Journal	Archive for Rational Mechanics and Analysis
Volume	237
Issue number	1
DOIs	https://doi.org/10.1007/s00205-020-01513-7
State	Published - 1 Jul 2020

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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 off the thermostat. To our surprise, even though the thermostat fluctuations are time-dependent, the scattering does not couple wave energy at various frequencies.",

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AB - 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 off the thermostat. To our surprise, even though the thermostat fluctuations are time-dependent, the scattering does not couple wave energy at various frequencies.

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High Frequency Limit for a Chain of Harmonic Oscillators with a Point Langevin Thermostat

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