Abstract

Recently, it has been shown that the two established heat conduction mechanisms—namely the propagation of atomic vibrational waves in anharmonic crystals elucidated by Peierls [1] and the couplings between atomic vibrational modes in harmonic glasses envisioned by Allen and Feldman [2]—naturally emerge as limiting cases of a unified theory, derived from the Wigner formulation of quantum mechanics and describing on an equal footing solids ranging from crystals to glasses [3].

Here, we rely on this unified theoretical framework to investigate what happens when atomic vibrational waves reach the Ioffe-Regel limit (i.e. their mean free paths become shorter than the interatomic spacing), showing that they can still contribute to heat transport due to their wave-like capability to interfere and tunnel. Then, we focus on signatures of the “hydrodynamic” regime of thermal transport, where heat conduction becomes fluid-like and Fourier’s diffusive equation fails. We show that the recent observation of temperature waves in this regime [4] can be explained using the “viscous heat equations” [5], thus we propose a strategy that uses resonance to amplify these temperature waves.

[1] R. Peierls, Ann. Phys. 395, 1055–1101 (1929)

[2] P. B. Allen and J. L. Feldman, Physical Review Letters 62, 645–648 (1989)

[3] M. Simoncelli, N. Marzari, and F. Mauri, Nature Physics, 15, 809 (2019).

[4] J. Jeong, X. Li, S. Lee, L. Shi, and Y. Wang, Physical Review Letters 127, 085901 (2021)

[5] M. Simoncelli, N. Marzari, and A. Cepellotti, Physical Review X 10 , 011019 (2020).