Fluctuation-induced forces in confined ideal and imperfect Bose gases

Fluctuation-induced ("Casimir") forces caused by thermal and quantum fluctuations are investigated for ideal and imperfect Bose gases confined to d-dimensional films of size infinity(d-1) x D under periodic (P), antiperiodic (A), Dirichlet-Dirichlet (DD), Neumann-Neumann (NN), and Robin (R) boundary conditions (BCs). The full scaling functions (sic)(d)(BC)(x(lambda) = D/lambda(th), x(xi) = D/xi) of the residual reduced grand potential per area phi(BC)(res,d)(T, mu, D) = D-(d-1)(sic)(d)(BC)(x(lambda), x(xi)) are determined for the ideal gas case with these BCs, where lambda(th) and xi are the thermal de Broglie wavelength and the bulk correlation length, respectively. The associated limiting scaling functions Theta(BC)(d)(x(xi)) equivalent to (sic)(d)(BC)(infinity, x(xi)) describing the critical behavior at the bulk condensation transition are shown to agree with those previously determined from a massive free O(2) theory for BC = P,A,DD,DN,NN. For d = 3, they are expressed in closed analytical form in terms of polylogarithms. The analogous scaling functions (sic)(d)(BC)(x(lambda), x(xi), c(1)D, c(2)D) and Theta(R)(d)(x(xi), c(1)D, c(2)D) under the RBCs (partial derivative(z) -c(1))phi|(z=0) = (partial derivative(z) + c(2))phi|(z=D) = 0 with c(1) >= 0 and c(2) >= 0 are also determined. The corresponding scaling functions (sic)(infinity,d)(P)(x(lambda), x(xi)) and Theta(P)(infinity,d)(x(xi)) for the imperfect Bose gas are shown to agree with those of the interacting Bose gas with n internal degrees of freedom in the limit n -> infinity. Hence, for d = 3, Theta(P)(infinity,d)(x(xi)) is known exactly in closed analytic form. To account for the breakdown of translation invariance in the direction perpendicular to the boundary planes implied by free BCs such as DDBCs, a modified imperfect Bose gas model is introduced that corresponds to the limit n -> infinity of this interacting Bose gas. Numerically and analytically exact results for the scaling function Theta(DD)(infinity,3)(x(xi)) therefore follow from those of the O(2n)phi(4) model for n -> infinity.