A microscopic model of ballistic-diffusive crossover

TL;DR

This paper develops a microscopic model explaining the transition from diffusive to ballistic heat transport in low-dimensional systems as their size decreases, providing a rigorous scaling law for the thermal current.

Contribution

It introduces a microscopic framework that captures both ballistic and diffusive regimes and derives a scaling law for the thermal current in one-dimensional systems.

Findings

Crossover occurs when system size matches a characteristic length scale.

Derived a rigorous scaling law for thermal current.

Unified microscopic description of heat transport regimes.

Abstract

Several low-dimensional systems show a crossover from diffusive to ballistic heat transport when system size is decreased. Although there is some phenomenological understanding of this crossover phenomena in the coarse grained level, a microscopic picture that consistently describes both the ballistic and the diffusive transport regimes has been lacking. In this work we derive a scaling from for the thermal current in a class of one dimensional systems attached to heat baths at boundaries, and show rigorously that the crossover occurs when the characteristic length scale of the system competes with the system size.