Hydrodynamics beyond local equilibrium: Application to electron gas

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Abstract
Generalized hydrodynamic theory, which does not rest on the requirement of a local equilibrium, is derived in the long-wave limit of a kinetic equation. The theory bridges the whole frequency range between the quasistatic (Navier-Stokes) hydrodynamics and the high-frequency (Vlasov) collisionless limit. In addition to pressure and velocity the theory includes new macroscopic tensor variables. In a linear approximation these variables describe an effective shear stress of a liquid and the generalized hydrodynamics recovers the Maxwellian theory of highly viscous fluids—the media behaving as solids on a short time scale, but as viscous fluids on long-time intervals. It is shown that the generalized hydrodynamics can be applied to the Landau theory of Fermi liquid. Illustrative results for collective modes in confined systems are given, which show that nonequilibrium effects qualitatively change the collective dynamics in comparison with the predictions of the heuristic Bloch’s hydrodynamics. Earlier improvements of the Bloch theory are critically reconsidered.
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