1211.1723 (Maksim Tomchenko)
Maksim Tomchenko
In the framework of the Gross--Pitaevskii approach, we have considered the interacting Bose gas in a one-dimensional bounded domain and have found two different dispersion laws for phonons. One law coincides with the well-known Bogolyubov one (h\omega(k))^2 =(h^2 k^2/2m)^2 + qn\nu(k)h^2 k^2/m with q=1. The second law is new and is described by the same formula with q=1/2. The first solution corresponds to the single harmonic (as for the cyclic boundaries), and the second solution is represented by the set of harmonics forming a wave packet centered at the given $k$. Two solutions appear due to two different combinations of harmonics in the wave packet.
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http://arxiv.org/abs/1211.1723
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