On the strong influence of boundaries on the bulk microstructure of a uniform interacting Bose gas

Abstract

It is usually assumed that the boundaries do not affect the bulk microstructure of an interacting uniform Bose gas. Therefore, the models use the most convenient cyclic boundary conditions. We show that, in reality, the boundaries affect strongly the bulk microstructure, by changing the ground-state energy E_0 and the energy of quasiparticles E(k). For the latter, we obtain the formula E^2 =(h^2 k^{2}/2m)^2 + 2^{-f}n\nu(k)(h^2 k^2/m) differing from the well-known Bogolyubov formula by the factor 2^{-f}, where f is the number of noncyclic coordinates. The Bogolyubov solution is also possible in the presence of boundaries, but it has a larger value of $E_{0}$ and should be unstable. The influence of boundaries is related to the topology.