We study a variant of Davies' model of heat conduction, consisting of a chain of (classical or quantum) harmonic oscillators, whose ends are coupled to thermal reservoirs at different temperatures, and where neighboring oscillators interact via intermediate reservoirs. In the weak coupling limit, we show that a unique stationary state exists, and that a discretized heat equation holds. We give an explicit expression of the stationary state in the case of two classical oscillators. The heat equation is obtained in the hydrodynamic limit, and it is proved that it completely describes the macroscopic behavior of the model. © 1985 Plenum Publishing Corporation.

The stationary state and the heat equation for a variant of Davies' model of heat conduction

Artuso R.;Frigerio A.;
1985-01-01

Abstract

We study a variant of Davies' model of heat conduction, consisting of a chain of (classical or quantum) harmonic oscillators, whose ends are coupled to thermal reservoirs at different temperatures, and where neighboring oscillators interact via intermediate reservoirs. In the weak coupling limit, we show that a unique stationary state exists, and that a discretized heat equation holds. We give an explicit expression of the stationary state in the case of two classical oscillators. The heat equation is obtained in the hydrodynamic limit, and it is proved that it completely describes the macroscopic behavior of the model. © 1985 Plenum Publishing Corporation.
1985
heat equation; local equilibrium; stationary state supporting a temperature-gradient; Weak coupling limit
Artuso, R.; Benza, V.; Frigerio, A.; Gorini, V.; Montaldi, E.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2146954
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