Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-08-27
Physics
Condensed Matter
Statistical Mechanics
8 pages, 7 figures
Scientific paper
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 non-conserving systems, there is no low frequency peak. The momentum non-conserving 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.
Dhar Abhishek
Kundu Anupam
Narayan Onuttom
Saito Keiji
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