The authors demonstrate that a superfluid flowing in a random potential can be identified with a uniform system at thermal equilibrium with an effective temperature due to random elastic scattering of the moving condensate by disorder.
This paper represents the full version of a paper published earlier in Physica A [246 (1997), 275]. The present paper includes argumentation, proofs and details omitted in the shortened version. The papers are a further development of the approach in quantum statistical mechanics proposed by the author. The hierarchy of equations for reduced density matrices obtained previously is extended to the case corresponding to the Bose-Einstein condensation. The relevant state of the system with a condensate can be superfluid as well as nonsuperfluid. Special attention is given to the thermodynamics of superfluid systems. According to the results of the papers superfluidity is the state of a fluid whose symmetry is spontaneously broken because of a stationary flow. The state corresponds to thermodynamic equilibrium while the magnitude of the flow depends upon the temperature and is determined by thermodynamic considerations. The equations obtained are solved in two simple cases. The physical origin of superfluidity, peculiarities of the phenomenon in closed volumes and the critical velocity are discussed as well.
Two-dimensional (2D) bosons can undergo a Kosterlitz-Thouless transition[1], which does not involve macroscopic occupation of a single quantum state, but which can still result in superfluidity. In addition, strongly interacting bosons subject to a random potential can also exhibit superfluidity, as in the case of charged superfluidity that occurs in high-T c superconductors. Competition between the strength of the interaction and the degree of potential disorder are among the many complicated and competing factors which determine whether superfluidity is promoted or supressed in a Bose system[2]. Strong potential disorder forces bosons to localize and can result in an insulating Bose glass phase. Alternatively, repulsive interactions among bosons act to release them from their traps, to keep their inter-particle distances as uniform as the potential allows, and to arrange the flow direction. An appropriate interaction strength can thus promote superfluidity.
The dynamics of interacting bosons in one dimension following the sudden switching on of a weak disordered potential is investigated. On time scales before quasiparticles scatter (prethermalized regime), the dephasing from random elastic forward scattering causes all correlations to decay exponentially fast, but the system remains far from thermal equilibrium. For longer times, the combined effect of disorder and interactions gives rise to inelastic scattering and to thermalization. A novel quantum kinetic equation accounting for both disorder and interactions is employed to study the dynamics. Thermalization turns out to be most effective close to the superfluid-Bose-glass critical point where nonlinearities become more and more important. The numerically obtained thermalization times are found to agree well with analytic estimates.