# On the Planckian bound for heat diffusion in insulators

## TL;DR

This paper proposes that the Planckian bound on heat diffusion in insulators arises from a quantum mechanical limit on sound velocity, linking thermal transport to fundamental physical constants and crystal properties.

## Contribution

It introduces a quantum mechanical bound on sound velocity that explains the Planckian bound on thermal transport in insulators, supported by analysis of various crystal classes.

## Key findings

- The Planckian bound is related to a sound velocity limit $v_s < v_M$.
- High-temperature thermal transport timescales are proportional to $v_M/v_s$.
- The velocity bound accounts for the observed Planckian bound in insulators.

## Abstract

High temperature thermal transport in insulators has been conjectured to be subject to a Planckian bound on the transport lifetime $\tau \gtrsim \tau_\text{Pl} \equiv \hbar/(k_B T)$, despite phonon dynamics being entirely classical at these temperatures. We argue that this Planckian bound is due to a quantum mechanical bound on the sound velocity: $v_s < v_M$. The `melting velocity' $v_M$ is defined in terms of the melting temperature of the crystal, the interatomic spacing and Planck's constant. We show that for several classes of insulating crystals, both simple and complex, $\tau/\tau_\text{Pl} \approx v_M/v_s$ at high temperatures. The velocity bound therefore implies the Planckian bound.