Effective binding potential from Casimir interactions: the case of the Bose gas

We consider the thermal Casimir effect in ideal Bose gases, where the disper-sion relation involves both terms quadratic and quartic in momentum. We demonstrate that if macroscopic objects are immersed in such a fluid in spatial dimensionality d ? {3,7, 11, ...} and at the critical temperature T-c, the Casimir force acting between them is characterized by a sign which depends on the separation D between the bodies and changes from attractive at large distances to repulsive at smaller separations. In consequence, an effective potential which binds the two objects at a finite separation arises. We demonstrate that for odd integer dimensionality d ? {3, 5, 7, ...}, the Casimir energy is a polynomial of degree (d - 1) in D-2. We point out a very special role of dimensionality d = 3, where we derive a strikingly simple form of the Casimir energy as a function of D at Bose-Einstein condensation. We discuss crossover between monoton-ous and oscillatory decay of the Casimir interaction above the condensation temperature.