Heat Flow in a Periodically Forced, Thermostatted Chain

We investigate the properties of a harmonic chain in contact with a thermal bath at one end and subjected, at its other end, to a periodic force. The particles also undergo a random velocity reversal action, which results in a finite heat conductivity of the system. We prove the approach of the system to a time periodic state and compute the heat current, equal to the time averaged work done on the system, in that state. This work approaches a finite positive value as the length of the chain increases. Rescaling space, the strength and/or the period of the force leads to a macroscopic temperature profile corresponding to the stationary solution of a continuum heat equation with Dirichlet-Neumann boundary conditions.

Automated summary

We study a harmonic chain in contact with a thermal bath, subjected to a periodic force at one end while undergoing random velocity reversals. This leads to a limited heat conductivity and the system approaches a time periodic state. We compute the heat current, which represents the time averaged work done on the system, and find that it approaches a finite positive value as the chain's length increases. By rescaling space and adjusting the strength and/or period of the force, we observe a macroscopic temperature profile consistent with the stationary solution of a continuum heat equation with Dirichlet-Neumann boundary conditions.