Abstract
The spatial fluctuations of a superfluid flowing in a weak random potential are investigated. We employ classical field theory to demonstrate that the disorder-averaged nonequilibrium second-order correlation of the order parameter at zero temperature is identical to the thermally averaged equilibrium counterpart of a uniform superfluid at an effective temperature. The physics behind this equivalence is that scattering of a moving condensate by disorder has the same effect on the correlation function as equilibrium thermal excitations. The correlation function exhibits an exponential decay in one dimension and a power-law decay in two dimensions. We show that the effective temperature can be measured in an interference experiment of ultracold atomic gases.
Highlights
The universality of thermodynamics and statistical mechanics is attributed to the fact that macroscopic states of equilibrium systems can be described by a few key parameters such as temperature and pressure
We argue that scattering of a moving condensate by disorder has the same effect as thermal excitations, and the superfluid flowing in a random potential can be identified with a uniform system at thermal equilibrium with an effective temperature
We have demonstrated that the nonequilibrium correlation of the U(1) order parameter of a superflow in a random medium has a one-to-one correspondence to the equilibrium correlation of a clean system at an effective temperature
Summary
The universality of thermodynamics and statistical mechanics is attributed to the fact that macroscopic states of equilibrium systems can be described by a few key parameters such as temperature and pressure. We demonstrate that the disorder-averaged nonequilibrium second-order correlation of the order parameter at zero temperature is identical to the thermally averaged equilibrium counterpart of a uniform superfluid at an effective temperature. The decay behavior of the disorder-averaged correlation in one and two dimensions is reminiscent of the Hohenberg-Mermin-Wagner theorem for a system with continuous symmetry, which states that the thermally averaged correlation of the order parameter decays in one and two dimensions [36,37,38] It is of fundamental importance in nonequilibrium statistical physics to understand how and when nonequilibrium driving destroys an ordered phase that is stable in equilibrium [39].
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