Broken Symmetry and Generalized Bose Condensation in Restricted Geometries

Abstract

It is suggested, on the basis of soluble models, that generalized Bose condensation results from a broken symmetry associated with a nonvanishing pairing amplitude with very large low‐momentum components, leading to a nonzero ``pairing density'' p_c as well as a nonzero generalized condensate density ρ_c. For systems of interacting bosons it is proved that (1) nonzero p_c implies nonzero ρ_c, and (2) p_c = 0 in one or two dimensions and, more generally, for geometries finite in one dimension and infinite in the other two (films) or finite in two dimensions and infinite in one (pores). It is pointed out that this does not exclude superfluidity in such geometries, but does show the need of a new mechanism to explain it.