Aspects of causal viscous hydrodynamics

We investigate the phenomenology of freely expanding fluids, with different material properties, evolving through the Israel-Stewart (IS) causal viscous hydrodynamics, and compare our results with those obtained in the relativistic Eckart-Landau-Navier-Stokes (ELNS) acausal viscous hydrodynamics. Through the analysis of scaling invariants we give a definition of thermalization time which can be self-consistently determined in viscous hydrodynamics. Next we construct the solutions for one-dimensional boost-invariant flows. Expansion of viscous fluids is slower than that of one-dimensional ideal fluids, resulting in entropy production. At late times, these flows are reasonably well approximated by solutions obtained in ELNS hydrodynamics. Estimates of initial energy densities from observed final values are strongly dependent on the dynamics one chooses. For the same material, and the same final state, IS hydrodynamics gives the smallest initial energy density. We also study fluctuations about these one-dimensional boost-invariant backgrounds; they are damped in ELNS hydrodynamics but can become sound waves in IS hydrodynamics. The difference is obvious in power spectra due to clear signals of wave-interference in IS hydrodynamics, which is completely absent in ELNS dynamics.Comment: 27 pages, 17 figures, references added, minor changes, version to appear in Phys. Rev. (C

Hydrodynamic theory of an electron gas

The generalised hydrodynamic theory of an electron gas, which does not rely on an assumption of a local equilibrium, is derived as the long-wave limit of a kinetic equation. Apart from the common hydrodynamics variables the theory includes the tensor fields of the higher moments of the distribution function. In contrast to the Bloch hydrodynamics, the theory leads to the correct plasmon dispersion and in the low frequency limit recovers the Navies-Stocks hydrodynamics. The linear approximation to the generalised hydrodynamics is closely related to the theory of highly viscous fluids.Comment: 4 pages, revte