Casimir Force between Two Vortices in a Turbulent Bose–Einstein Condensate

We consider the Casimir force between two vortices due to the presence of density fluctuations induced by turbulent modes in a Bose–Einstein condensate. We discuss the cases of unbounded and finite condensates. Turbulence is described as a superposition of elementary excitations (phonons or BdG modes) in the medium. Expressions for the Casimir force between two identical vortex lines are derived, assuming that the vortices behave as point...