Abstract
Fluctuation-induced (“Casimir”) forces caused by thermal and quantum fluctuations are investigated for ideal and imperfect Bose gases confined to -dimensional films of size under periodic (P), antiperiodic (A), Dirichlet-Dirichlet (DD), Neumann-Neumann (NN), and Robin (R) boundary conditions (BCs). The full scaling functions of the residual reduced grand potential per area are determined for the ideal gas case with these BCs, where and are the thermal de Broglie wavelength and the bulk correlation length, respectively. The associated limiting scaling functions describing the critical behavior at the bulk condensation transition are shown to agree with those previously determined from a massive free theory for . For , they are expressed in closed analytical form in terms of polylogarithms. The analogous scaling functions and under the RBCs with and are also determined. The corresponding scaling functions and for the imperfect Bose gas are shown to agree with those of the interacting Bose gas with internal degrees of freedom in the limit . Hence, for 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 of this interacting Bose gas. Numerically and analytically exact results for the scaling function therefore follow from those of the model for .
- Received 29 March 2017
- Revised 15 May 2017
DOI:https://doi.org/10.1103/PhysRevE.95.062112
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