Diffusive Heat Waves in Random Conformal Field Theory

TL;DR

This paper introduces a conformal field theory model with random velocities to describe heat transport in disordered one-dimensional quantum systems, revealing how impurities induce diffusive behavior in heat waves.

Contribution

It provides an exact analytical framework for understanding how static impurities cause diffusive contributions in heat transport within a CFT model.

Findings

Impurities lead to both normal and anomalous diffusion in heat waves.

Derived impurity-averaged Green's functions for energy density and heat current.

Explicit formula for thermal conductivity showing a universal peak and impurity-dependent contributions.

Abstract

We propose and study a conformal field theory (CFT) model with random position-dependent velocity that, as we argue, naturally emerges as an effective description of heat transport in one-dimensional quantum many-body systems with certain static random impurities. We present exact analytical results that elucidate how purely ballistic heat waves in standard CFT can acquire normal and anomalous diffusive contributions due to our impurities. Our results include impurity-averaged Green's functions describing the time evolution of the energy density and the heat current, and an explicit formula for the thermal conductivity that, in addition to a universal Drude peak, has a nontrivial real regular contribution that depends on details of the impurities.