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arXiv · 1908.04792

On the Planckian bound for heat diffusion in insulators

Connie H. Mousatov·Sean A. Hartnoll
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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.

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Connie H. Mousatov, Sean A. Hartnoll. 2019-08-13. On the Planckian bound for heat diffusion in insulators. https://doi.org/10.1038/s41567-020-0828-6

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