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Abstract: An exact linear response expression is obtained for the heat current in aclassical Hamiltonian system coupled to heat baths with time-dependenttemperatures. The expression is equally valid at zero and finite frequencies.We present numerical results on the frequency dependence of the responsefunction for three different one-dimensional models of coupled oscillatorsconnected to Langevin baths with oscillating temperatures. For momentumconserving systems, a low frequency peak is seen that, is higher than the zerofrequency response for large systems. For momentum non-conserving systems,there is no low frequency peak. The momentum non-conserving system is expectedto satisfy Fourier-s law, however, at the single bond level, we do not see anyclear agreement with the predictions of the diffusion equation even at lowfrequencies. We also derive an exact analytical expression for the response ofa chain of harmonic oscillators to a not necessarily small temperaturedifference; the agreement with the linear response simulation results for thesame system is excellent.



Autor: Abhishek Dhar, Onuttom Narayan, Anupam Kundu, Keiji Saito

Fuente: https://arxiv.org/







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