Incorporate nonlinear effects into full-Boltzmann phonon hydrodynamics

Incorporate nonlinear advection and other nonlinear transport effects into analytical and numerical phonon-hydrodynamic descriptions while retaining the full collision matrix of the phonon Boltzmann transport equation.

Background

The viscous heat equations and current exact Monte Carlo solvers for the linearized Boltzmann transport equation operate in the close-to-equilibrium linear regime and therefore omit nonlinear advection terms. Existing nonlinear treatments are based on simplifying approximations, including the Callaway model, relaxation-time approximations, weakly nonlinear continuum theories, or thermomass formulations that are not derived from the full phonon collision operator.

A general treatment that preserves the full mode-coupling structure of the Boltzmann collision matrix would be needed to describe nonlinear phonon hydrodynamics microscopically and beyond the laminar linear-response regime. The review explicitly identifies this as unresolved and outside its scope.