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, USA
https://www.apam.columbia.edu/michele-simoncelli

The thermal fingerprint of a single superconducting vortex expelled from the box with a short current pulse
Fig. Illustration of the structure of different type of solids.

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.