Energy repartition for a harmonic chain with local reservoirs

TL;DR

This paper provides an exact analysis of vibrational properties and energy distribution in a harmonic chain with local heat baths, revealing mode-dependent temperature profiles and fluctuation control via bath temperature design.

Contribution

It introduces an exact solution for nonequilibrium steady states in harmonic chains with local reservoirs, highlighting mode-temperature independence from interaction strength.

Findings

Mode temperatures are independent of harmonic interaction and damping.

Energy distribution varies among modes based on bath temperatures and boundary conditions.

Bath-temperature profiles can be engineered to control fluctuations at specific frequencies.

Abstract

We exactly analyze the vibrational properties of a chain of harmonic oscillators in contact with local Langevin heat baths. Nonequilibrium steady-state fluctuations are found to be described by a set of mode-temperatures, independent of the strengths of both the harmonic interaction and the viscous damping. Energy is equally distributed between the conjugate variables of a given mode but differently among different modes, in a manner which depends exclusively on the bath temperatures and on the boundary conditions. We outline how bath-temperature profiles can be designed to enhance or reduce fluctuations at specific frequencies in the power spectrum of the chain length.