EPFL Doctorate Award - 2022 - Michele Simoncelli
Thermal transport beyond Fourier, and beyond Boltzmann
EPFL thesis n°8158
Thesis director: Prof. N. Marzari
For the development of novel microscopic and mesoscopic theories of thermal transport: the Wigner transport equation, generalizing Peierls-Boltzmann, and the viscous heat equations, generalizing Fourier's law.
Crystals and glasses exhibit fundamentally different heat-conduction mechanisms: the periodicity of crystals allows for the excitation of atomic vibrations that propagate like particles and carry heat, as first discussed by Peierls in 1929; in glasses, instead, the lack of periodicity breaks Peierls’s picture and heat behaves wave-like, diffusing via a wave-like tunneling between atomic vibrational modes, often described by a harmonic theory introduced by Allen and Feldman in 1989.
In this thesis, we developed a unified microscopic equation that describes on an equal footing heat conduction in crystals, glasses, and anything in-between. In particular, it predicts correctly and in agreement with experiments the thermal conductivity in crystals, glasses, and most importantly in the mixed regime of complex crystals with ultra-low or glass-like conductivity.
In practice, this equation has found straightforward applications in the aerospace industry and in the field of renewable energy, setting the stage to systematically engineer thermal barrier coatings, and to enhance the efficiency of devices used for thermoelectric conversion of waste heat into electricity.
We also showed how in the crystalline regime such a microscopic transport equation can be coarse-grained into a set of “viscous heat equations” that generalize Fourier's macroscopic equation, accounting for both diffusion and heat hydrodynamics, and rationalize the recent discovery of heat transfer via temperature waves in devices made of graphite.