Repulsive Casimir forces at quantum criticality

We study the Casimir effect in the vicinity of a quantum critical point. As a prototypical system we analyze the $d$-dimensional imperfect (mean-field) Bose gas enclosed in a slab of extension $L^{d-1}\times D$ and subject to periodic boundary conditions. The thermodynamic state is adjusted so that $L\ggλ\gg D\ggł_{mic}$, where $λ\sim T^{-1/2}$ is the thermal de Broglie length, and $l_{mic}$ denotes microscopic lengthscales. Our exact analysis indicates that the Casimir force in the above specified regime is generically repulsive and decays either algebraically or exponentially, with a non-universal amplitude.

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