phononhydrodynamic

Phonon hydrodynamics is a framework for describing heat transport in insulators and some semiconductors where phonons behave as a collective, fluid-like medium. This hydrodynamic regime arises when momentum-conserving normal (N) phonon-phonon scattering dominates over momentum-relaxing processes such as Umklapp (U) scattering and boundary scattering. Under these conditions crystal momentum is approximately conserved for relatively long times, enabling a continuum, hydrodynamic description in terms of local energy and momentum densities and fluxes.

The theory starts from the phonon Boltzmann transport equation; in the hydrodynamic limit it yields continuity equations for energy and momentum and a Navier–Stokes–like equation for the phonon flow, with coefficients such as viscosity and thermal conductivity. The framework predicts phenomena beyond Fourier diffusion, including temperature waves (second sound) and Poiseuille flow of heat in narrow channels.

Realizations and evidence: hydrodynamic phonon transport has been explored in dielectric crystals like NaF at low temperatures and in layered materials such as graphite, with theoretical extensions to other systems including boron arsenide and graphene under suitable conditions. Distinctive signatures include nonlocal heat transport, enhanced thermal conduction beyond diffusive limits, and, in some regimes, the appearance of second sound.

Impact and scope: phonon hydrodynamics helps explain size- and geometry-dependent thermal transport in nanoscale devices and informs the design of materials with tailored thermal properties. It remains an active area of research at the crossroads of condensed matter physics and materials science, advancing understanding of fundamental heat transport mechanisms.