TY - JOUR

T1 - Linear-response formula for finite-frequency thermal conductance of open systems

AU - Dhar, Abhishek

AU - Narayan, Onuttom

AU - Kundu, Anupam

AU - Saito, Keiji

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011/1/3

Y1 - 2011/1/3

N2 - An exact linear-response expression is obtained for the heat current in a classical Hamiltonian system coupled to heat baths with time-dependent temperatures. The expression is equally valid at zero and finite frequencies. We present numerical results on the frequency dependence of the response function for three different one-dimensional models of coupled oscillators connected to Langevin baths with oscillating temperatures. For momentum conserving systems, a low-frequency peak is seen that is higher than the zero-frequency response for large systems. For momentum nonconserving systems, there is no low-frequency peak. The momentum nonconserving system is expected to satisfy Fourier's law; however, at the single bond level, we do not see any clear agreement with the predictions of the diffusion equation even at low frequencies. We also derive an exact analytical expression for the response of a chain of harmonic oscillators to a (not necessarily small) temperature difference; the agreement with the linear-response simulation results for the same system is excellent.

AB - An exact linear-response expression is obtained for the heat current in a classical Hamiltonian system coupled to heat baths with time-dependent temperatures. The expression is equally valid at zero and finite frequencies. We present numerical results on the frequency dependence of the response function for three different one-dimensional models of coupled oscillators connected to Langevin baths with oscillating temperatures. For momentum conserving systems, a low-frequency peak is seen that is higher than the zero-frequency response for large systems. For momentum nonconserving systems, there is no low-frequency peak. The momentum nonconserving system is expected to satisfy Fourier's law; however, at the single bond level, we do not see any clear agreement with the predictions of the diffusion equation even at low frequencies. We also derive an exact analytical expression for the response of a chain of harmonic oscillators to a (not necessarily small) temperature difference; the agreement with the linear-response simulation results for the same system is excellent.

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U2 - 10.1103/PhysRevE.83.011101

DO - 10.1103/PhysRevE.83.011101

M3 - Article

AN - SCOPUS:78651429595

VL - 83

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 1

M1 - 011101

ER -