Classical and quantum harmonic mean-field models coupled intensively and extensively with external baths

TL;DR

This paper analyzes the nonequilibrium steady states of large quantum harmonic oscillator networks coupled to thermal baths, revealing size-dependent temperature behaviors, quantum effects at low temperatures, and unique decoupling phenomena.

Contribution

It provides analytical expressions for heat fluxes and temperature distributions in large quantum networks with different coupling regimes, highlighting novel size and quantum effects.

Findings

Bulk temperature vanishes in the thermodynamic limit.

Quantum effects are significant only below a temperature that decreases with system size.

Energy flux at low temperatures follows the universal quantum of thermal conductance.

Abstract

We study the nonequilibrium steady-state of a fully-coupled network of $N$ quantum harmonic oscillators, interacting with two thermal reservoirs. Given the long-range nature of the couplings, we consider two setups: one in which the number of particles coupled to the baths is fixed (intensive coupling) and one in which it is proportional to the size $N$ (extensive coupling). In both cases, we compute analytically the heat fluxes and the kinetic temperature distributions using the nonequilibrium Green's function approach, both in the classical and quantum regimes. In the large $N$ limit, we derive the asymptotic expressions of both quantities as a function of $N$ and the temperature difference between the baths. We discuss a peculiar feature of the model, namely that the bulk temperature vanishes in the thermodynamic limit, due to a decoupling of the dynamics of the inner part of the system from the baths. At variance with usual cases, this implies that the steady state depends on the initial state of the particles in the bulk. We also show that quantum effects are relevant only below a characteristic temperature that vanishes as $1/N$. In the quantum low-temperature regime the energy flux is proportional to the universal quantum of thermal conductance.