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

الأصل · EN

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 E₀ and the energy of quasiparticles E(k). For the latter, we obtain the formula E² =(h² k²/2m)² + 2⁻ᶠnν(k)(h² k²/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 E₀ and should be unstable. The influence of boundaries is related to the topology.