Application of the Hilbert Space Average Method on Heat Conduction Models

TL;DR

This paper applies the Hilbert space average method to analyze heat conduction in quantum chains, demonstrating that energy diffusion and Fourier's law emerge from reversible quantum dynamics under certain conditions.

Contribution

It introduces the use of HAM to predict energy diffusion and derive heat conduction coefficients in quantum chains, linking microscopic reversible dynamics to macroscopic heat transport.

Findings

Energy diffusion predicted by HAM in quantum chains.

Derivation of heat conduction coefficient near equilibrium.

Confirmation that Fourier's law follows from quantum reversible dynamics.

Abstract

We analyze closed one-dimensional chains of weakly coupled many level systems, by means of the so-called Hilbert space average method (HAM). Subject to some concrete conditions on the Hamiltonian of the system, our theory predicts energy diffusion with respect to a coarse-grained description for almost all initial states. Close to the respective equilibrium we investigate this behavior in terms of heat transport and derive the heat conduction coefficient. Thus, we are able to show that both heat (energy) diffusive behavior as well as Fourier's law follows from and is compatible with a reversible Schroedinger dynamics on the complete level of description.