Anomalous heat equation in a system connected to thermal reservoirs

TL;DR

This paper investigates anomalous heat transport in a one-dimensional system with thermal reservoirs, deriving exact solutions for temperature profiles and correlations, revealing non-local dynamics unlike classical diffusion.

Contribution

It introduces an exact analytical framework for anomalous heat conduction in a 1D system with reservoirs, highlighting non-local effects absent in Fourier's law.

Findings

Exact expressions for steady-state temperature and correlations

Demonstration of non-local anomalous heat equation governing evolution

Numerical verification of theoretical results

Abstract

We study anomalous transport in a one-dimensional system with two conserved quantities in presence of thermal baths. In this system we derive exact expressions of the temperature profile and the two point correlations in steady state as well as in the non-stationary state where the later describes the relaxation to the steady state. In contrast to the Fourier heat equation in the diffusive case, here we show that the evolution of the temperature profile is governed by a non-local anomalous heat equation. We provide numerical verifications of our results.