  We study the equilibrium statics and nonequilibrium driven dynamics of flux
line liquids in presence of a random pinning potential. Under the assumption of
replica symmetry, we find in the static case using a replica Gaussian
variational method that the only effect of disorder is to increase the tilt
modulus and the confining "mass" of the internal modes of the flux lines, thus
decreasing their thermal wandering. In the nonequilibrium, driven case, we
derive the long scale, coarse-grained equation of motion of the vortices in
presence of disorder, which apart from new Kardar-Parisi-Zhang nonlinearities,
has the same form as the equation of motion for unpinned vortices, with
renormalized coefficients. This implies, in particular, that the structure
factor of a disordered vortex liquid has the same functional form as in the
absence of pinning, in disagreement with the results of previous hydrodynamic
methods. The expression of the static structure factor derived within our
approach is consistent both with experimental data and with the standard theory
of elasticity of vortex lattices.
