Perturbative hydrodynamic Gross-Pitaevskii treatment for Bose-Einstein condensate in infinite length ring with disorder

For the derivation of the dilute Bose-Einstein condensate density and its phase, we have developed the perturbative approach for the solution of the stationary state couple Gross-Pitaevskii hydrodynamic equations. The external disorder potential is considered as a small parameter in this approach. We have derived expressions for the total density, condensate density, condensate density depletion and superfluid velocity of the Bose-Einstein condensate in an infinite length ring with disorder potential having a general form. For the delta correlated disorder, the explicit analytical forms of these quantities (except the superfluid velocity) have been obtained.

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