Crossover from ballistic to diffusive thermal transport in quantum Langevin dynamics study of a harmonic chain connected to self-consistent reservoirs

TL;DR

This study uses quantum Langevin dynamics to precisely analyze how thermal transport in a harmonic chain transitions from ballistic to diffusive, with self-consistent reservoirs determining interior temperatures and revealing an emergent mean free path.

Contribution

It provides an exact quantum dynamical analysis of the crossover from ballistic to diffusive heat transport in a harmonic chain with self-consistent reservoirs, highlighting the natural emergence of a mean free path.

Findings

Demonstrates crossover from ballistic to diffusive transport

Identifies the emergence of an effective mean free path

Uses exact quantum Langevin dynamics analysis

Abstract

Through an exact analysis using quantum Langevin dynamics, we demonstrate the crossover from ballistic to diffusive thermal transport in a harmonic chain with each site connected to Ohmic heat reservoirs. The temperatures of the two heat baths at the boundaries are specified from before whereas the temperatures of the interior heat reservoirs are determined self-consistently by demanding that in the steady state, on average, there is no heat current between any such (self-consistent) reservoir and the harmonic chain. Essence of our study is that the effective mean free path separating the ballistic regime of transport from the diffusive one emerges naturally.