Self-Consistent Mode-Coupling Approach to 1D Heat Transport

TL;DR

This paper develops an analytical and numerical framework for understanding heat transport in one-dimensional systems, proposing that the universality class depends on the dominant nonlinear interaction and clarifying the link between anomalous heat conductivity and diffusion.

Contribution

It introduces a self-consistent mode-coupling approach to analyze 1D heat transport, offering new insights into the universality class and the memory kernel's role.

Findings

Universality class depends on the leading order of nonlinear potential

Derived explicit form of the memory kernel

Connected anomalous heat conductivity with anomalous diffusion

Abstract

In the present Letter we present an analytical and numerical solution of the self-consistent mode-coupling equations for the problem of heat conductivity in one-dimensional systems. Such a solution leads us to propose a different scenario to accomodate the known results obtained so far for this problem. More precisely, we conjecture that the universality class is determined by the leading order of the nonlinear interaction potential. Moreover, our analysis allows us determining the memory kernel, whose expression puts on a more firm basis the previously conjectured connection between anomalous heat conductivity and anomalous diffusion.