Physics – Condensed Matter – Quantum Gases
Scientific paper
2012-04-10
Physics
Condensed Matter
Quantum Gases
4 pages
Scientific paper
It is usually assumed that the boundaries do not affect the bulk microstructure of a 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(k) =\sqrt{(h^{2} k^{2}/2m)^2 + (n\nu(k)/2^f)(h^2 k^2/m)} differing from the well-known Bogolyubov formula by the factor 1/2^f, where f is the number of noncyclic coordinates. The influence of boundaries is related to the topology, namely to the difference of the sets of oscillatory eigenmodes for closed and open systems.
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