Prof. Michele Simoncelli1
Talk: "Unified theories of transport in solids: from crystals to glasses, and from diffusion to viscous hydrodynamics"
1Department of Applied Physics and Applied Mathematics, Columbia University, New York, USAhttps://www.apam.columbia.edu/michele-simoncelli

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 underpinning their macroscopic conduction properties, formally extending established formulations [1,2] and developing the computational framework to solve them. Starting from a density-matrix formalism, I will show how the semiclassical particlelike Boltzmann equation is missing a wavelike tunneling term that becomes pivotal in disordered or defective materials [3]. The resulting unified formulation encompasses traditional particlelike and wavelike transport theories for crystals and glasses4 as special limits; most importantly, it overcomes their limitations, predicting hybrid crystal-glass heat conductivity anomalies that have been recently confirmed experimentally [5]. Finally, I will discuss how the microscopic transport equations for electrons [6] and phonons [2] can be coarse-grained into mesoscopic, viscous thermoelectric equations; these transcend ordinary diffusion, rationalizing the recent observation of hydrodynamic behavior and paving the way for its control and technological exploitation.
- [1] M. Simoncelli, N. Marzari, and F. Mauri, Unified theory of thermal transport in crystals and glasses, Nature Physics 15, 809–813 (2019).
- [2] M. Simoncelli, N. Marzari, and A. Cepellotti, Generalization of Fourier’s Law into Viscous Heat Equations, Physical Review X 10, 011019 (2020).
- [3] M. Simoncelli, N. Marzari, and F. Mauri, Wigner Formulation of Thermal Transport in Solids, Physical Review X 12, 041011 (2022).
- [4] M. Simoncelli, F. Mauri, and N. Marzari, Thermal conductivity of glasses: first-principles theory and applications, npj Computational Materials 9, 1–22 (2023).
- [5] M. Simoncelli, D. Fournier, M. Marangolo, E. Balan, K. Béneut, B. Baptiste, B. Doisneau, N. Marzari, and F. Mauri, Temperature-invariant crystal–glass heat conduction: From meteorites to refractories, Proceedings of the National Academy of Sciences 122 (2025).
- [6] J. Coulter, B. Rajkov, and M. Simoncelli, Coupled electron-phonon hydrodynamics and viscous thermoelectric equations (2025), arXiv:2503.07560.