Analog model for Euclidean wormholes: Bose–Einstein condensate with dirty surfaces

In this paper, we study a Bose–Einstein condensate under the effects of the noncondensate atomic cloud. We model the resulting linear interaction of the condensate with the atomic gas as a quenched disorder. Using the distributional zeta function method, we obtain a representation for the quenched free energy as a series of integral moments of the partition function. Assuming that the Bose–Einstein condensate is confined between two planar surfaces, we show that random surface fields generate nonlocal terms in the effective action. The nonlocal effects in this condensed matter system define an analog model of a Euclidean wormhole. The leading contribution of the nonlocal interactions to the Casimir pressure is obtained.