Unified theories of transport in solids: from crystals to glasses, and from diffusion to viscous hydrodynamics

Crystals and glasses have dramatically different properties which intrigued scientists long before the development of atomistic theories, and nowadays play a pivotal role in a variety of technologies. I will explore the quantum mechanisms that determine the macroscopic conduction properties of solids, extending established formulations and developing the computational framework to solve them. Starting from a density-matrix formalism, I will show how the semiclassical Boltzmann equation for heat transport is missing a tunneling term that becomes pivotal in disordered or defective materials. Second, I will discuss how this formulation can be extended to describe coupled transport phenomena — involving, e.g., heat and light, charge, or spin — which are critical for applications ranging from zero-carbon jet engines to neuromorphic computing. Finally, I will elucidate how the microscopic transport equations can be coarse-grained into mesoscopic, viscous equations; these transcend ordinary diffusion, rationalizing the recent observation of hydrodynamic behavior and paving the way for its control and technological exploitation.