Heat transport through a quantum Brownian harmonic chain beyond the weak-coupling regime: An exact treatment

TL;DR

This paper derives an exact expression for heat transport in a quantum harmonic chain beyond weak coupling, revealing how intra-coupling strength influences heat current and Fourier's law violation.

Contribution

It provides a novel exact solution for steady-state heat current in a quantum chain beyond weak coupling, exploring non-Markovian effects and resonance phenomena.

Findings

Heat current is small and N-independent in weak coupling, violating Fourier's law.

Increasing intra-coupling amplifies heat current, peaking at a resonant value.

Heat current decreases with chain length, showing N-independence for large N.

Abstract

We consider a linear chain of quantum harmonic oscillators, in which the number of the individual oscillators is given by an arbitrary number N, and each oscillator is coupled at an arbitrary strength kappa to its nearest neighbors ("intra-coupling"), as well as the two end oscillators of the chain are coupled at an arbitrary strength c_nu to two separate baths at arbitrarily different temperatures, respectively. We derive an exact closed expression for the steady-state heat current flowing from a hot bath through the chain to a cold bath, in the Drude-Ullersma damping model going beyond the Markovian damping. This allows us to explore the behavior of heat current relative to the intra-coupling strength as a control parameter, especially in pursuit of the heat power amplification. Then it turns out that in the weak-coupling regime (kappa, c_nu << 1), the heat current is small, as expected, and almost independent of chain length N, hence violating Fourier's law of heat conduction; this is consistent to the earlier results obtained within the rotating wave approximation for the intra-coupling as well as in the Born-Markov approximation for the chain-bath coupling. Beyond the weak-coupling regime, on the other hand, we typically observe that with increase of the intra-coupling strength the heat current is gradually amplified, and reaches its maximum value at some specific coupling strength kappa_R "resonant" to a given chain-bath coupling strength. Also, the behavior of heat current versus chain length appears typically in such a way that the magnitude of current reaches its maximum with N=1 and then gradually decreases with increase of the chain length, being in fact almost N-independent in the range of N large enough. As a result, Fourier's law proves violated also in this regime.