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 surface waves is tantamount to the GP 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.