Abstract. -We study the Casimir effect for the perfect Bose-gase in the slab geometry for various boundary conditions. We show that the grand canonical potential per unit area at the bulk critical chemical potential µ = 0 has the standard asymptotic form with universal Casimir terms.In contrast to the well-known Casimir effect for the photon gas, see e.g.[1], this effect for the massive quantum particles (quantum gases) is much less explored. In the present letter we consider the case of the perfect Bose-gas. The perfect Bose-gas is the simplest quantum mechanical system showing the spontaneous breaking of a continuous symmetry (Bose-Einstein condensation) for which the Casimir effect should appear. To our knowledge, this has surprisingly not been studied before.We first recall the definition of the Casimir amplitude at critical points or for phases with broken symmetry [2] [3]. Let

Abstract. We present a method of computing the Coulomb forces on particles in an infinite configuration of charges in one dimension, The resolution of the apparent nonuniqueness in this problem leads to a structural proof of the translation symmetry breaking in jellium, at all temperatures, and to a related phenomenon of phase nonuniqueness in the two component system. The appropriate generalizations of the DLR and KMS conditions for these states are discussed.

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No abstract

The attention of the reader is drawn to several misprints which may obscure the understanding of our paper(l~:Page 599, line 15 should read: "We assume that the decay in time of Cl(t) and C2(t) is O(1/tl+O, r/ > 0, for t-+ m."Page 599, the argument of the first 6"2 function occurring on the righthand side of formula (47) should be -t (and not + t).Page 611, Figs. 2a and 2b should be interchanged. Page 611, the last line of Section 4.2 should read C = 1, ~ = 1, /~ = 4 (which gives/3c = 0.549) REFERENCE 1. E. Buffet and Ph. A. Martin, Jr. Stat. Phys. 18:585 (1978).