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

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