Fourier's Law from Schroedinger Dynamics

TL;DR

This paper develops a theoretical framework predicting energy diffusion in one-dimensional quantum chains of weakly coupled systems, verified through numerical solutions of the Schrödinger equation, and relates it to heat conduction properties.

Contribution

It introduces a new theory linking Hamiltonian conditions to energy diffusion and heat conduction in quantum chains, supported by numerical verification.

Findings

Energy diffusion occurs for most initial states under certain Hamiltonian conditions.

Numerical simulations confirm the theoretical predictions.

Heat conduction coefficient can be derived from the theory near equilibrium.

Abstract

We consider a class of one-dimensional chains of weakly coupled many level systems. We present a theory which predicts energy diffusion within these chains for almost all initial states, if some concrete conditions on their Hamiltonians are met. By numerically solving the time dependent Schroedinger equation, we verify this prediction. Close to equilibrium we analyze this behavior in terms of heat conduction and compute the respective coefficient directly from the theory.