TY - JOUR

T1 - Heat Flow in a Periodically Forced, Thermostatted Chain

AU - Komorowski, Tomasz

AU - Lebowitz, Joel L.

AU - Olla, Stefano

N1 - Publisher Copyright: © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2023/6

Y1 - 2023/6

N2 - 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.

AB - 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.

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U2 - https://doi.org/10.1007/s00220-023-04654-4

DO - https://doi.org/10.1007/s00220-023-04654-4

M3 - Article

SN - 0010-3616

VL - 400

SP - 2181

EP - 2225

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 3

ER -