Linear response formula for finite frequency thermal conductance of open systems

Abstract

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.

8 pages, 7 figures

References in corpus (6)

• Heat Transport in low-dimensional systems
• Heat transport in harmonic lattices
• Ratcheting Heat Flux against a Thermal Bias
• Energy carriers in the Fermi-Pasta-Ulam $\beta$ lattice: Solitons or Phonons?
• Emergence and control of heat current from strict zero thermal bias
• Green-Kubo formula for heat conduction in open systems

Cited by in corpus (6)

• Dynamic control of quantum geometric heat flux in a nonequilibrium spin-boson model
• Geometric Heat Flux for Classical Thermal Transport in Interacting Open Systems
• Classifying transport behavior via current fluctuations in open quantum systems
• Theory of the Dynamical Thermal conductivity of Metals
• Dynamical crossovers and correlations in a harmonic chain of active particles
• Linear response formula for open systems