Modeling of Bose-Einstein condensation in a water tank

Abstract

A theoretical basis for the possibility to emulate Bose-Einstein condensates (BEC) in a water tank is elaborated. It is shown that the equation governing the mean-field BEC dynamics, viz., the Gross-Pitaevskii (GP) equation, can be derived in the same form for surface water waves in a tank with a spatially varying background current. Depending on the wavenumber of the carrier wave, the GP equation for the surfacewaves is tantamount to theGP equation corresponding to the attractive or repulsive inter-atomic interactions in BEC. The external potential in the effective GP equation can be easily implemented in the water tank with an uneven bottom featuring a well or hump. Examples of particular stable exact solutions of the GP equation with the effective potential are presented. Estimates for physical parameters of the hydrodynamic setting are given.