Dr. Enrico Di Lucente1

Talk: "Theoretical and computational advances in quantum and hydrodynamic thermal transport"

1Theory and Simulation of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland

This talk addresses quantum and hydrodynamic thermal transport in crystalline systems, emphasizing regimes where conventional approaches face intrinsic limitations at microscopic and mesoscopic scales.

At the microscopic level, thermal conductivity arises from phonon drift and scattering, commonly described by the Boltzmann Transport Equation (BTE). Its Fermi’s Golden Rule (FGR)-based collisional term lacks a rigorous derivation and fails when phonon energy-variation scales approach collisional broadening, causing poor convergence, violations of detailed balance, and unphysical negative eigenvalues. A space–time-dependent BTE derived [1] from the Kadanoff–Baym Equations (KBE) overcomes these issues through a beyond-FGR formulation incorporating collisional broadening and energy-nonconserving scattering, while a hierarchy of Green’s- and spectral-function ansätze enables systematic extensions toward quantum-accurate transport. First-principles calculations show this resolves two longstanding FGR failures: (i) convergence problems in heat conductors and (ii) universal overdamping of flexural modes in 2D materials.

At the mesoscopic scale, viscous behavior can signal the onset of phonon hydrodynamics, which arises when momentum-conserving phonon collisions dominate. This regime is described by the viscous heat equations (VHE) [2], closely analogous to laminar Navier–Stokes equations (NSE). Reformulating the VHE as analytically solvable modified biharmonic equations for the velocity potential and stream function [3] allows them to be unified into a complex potential that defines flow streamlines, revealing two distinct temperature contributions linked to thermal compressibility and vorticity. Analysis of the irrotational and incompressible limits highlights parallels with electron fluid NSE, while extensions capture electron compressible regimes where drift velocities exceed plasmonic velocities. Applications to 2D graphite strip devices show how boundary conditions and transport coefficients can give rise to thermal vortices, negative thermal resistance, and heat backflow. These results provide powerful analytical tools for designing hydrodynamic phonon flow, generalize to electron systems, and open new directions for experimental exploration.

  • [1] E. Di Lucente, N. Marzari and Michele Simoncelli, Phonon collisional broadening and heat transport beyond the Boltzmann equation , to be submitted (2025).
  • [2] M. Simoncelli, N. Marzari, and A. Cepellotti, Generalization of Fourier’s Law into Viscous Heat Equations , Physical Review X 10, 011019 (2020).
  • [3] E. Di Lucente, F. Libbi and N. Marzari, Vortices and backflow in hydrodynamic heat transport. arXiv preprint arXiv:2501.16580 , (2025) – under second round of review in Physical Review Letters.