Superfluid bosons and flux liquids: disorder, thermal fluctuations, and finite-size effects

The influence of different types of disorder (both uncorrelated and correlated) on the superfluid properties of a weakly interacting or dilute Bose gas, as well as on the corresponding quantities for flux line liquids in high-temperature superconductors at low magnetic fields are reviewed, investigated and compared. We exploit the formal analogy between superfluid bosons and the statistical mechanics of directed lines, and explore the influence of the different ''imaginary time'' boundary conditions appropriate for a flux line liquid. For superfluids, we discuss the density and momentum correlations, the condensate fraction, and the normal-fluid density as function of temperature for two- and three-dimensional systems subject to a space- and time-dependent random potential as well as conventional point-, line-, and plane-like defects. In the case of vortex liquids subject to point disorder, twin boundaries, screw dislocations, and various configurations of columnar damage tracks, we calculate the corresponding quantities, namely, density and tilt correlations, the ''boson'' order parameter, and the tilt modulus. The finite-size corrections due to periodic vs. open ''imaginary time'' boundary conditions differ in interesting and important ways. Experimental implications for vortex lines are described briefly.