Dispersion law for a one-dimensional weakly interacting Bose gas with zero boundary conditions

Abstract

From the time-dependent Gross equation, we find the quasiparticle dispersion law for a one-dimensional weakly interacting Bose gas with a non-point interatomic potential and zero boundary conditions (BCs). The result coincides with the dispersion law for periodic BCs, i.e. the Bogolyubov law $E_B(k)=\sqrt{{\left(\frac{{\hslash }^2{k}^2}{2m}\right)}^2+n_0\nu (k)\frac{{\hslash }^2{k}^2}{m}}$. In the case of periodic BCs, the dispersion law can be easily derived from Gross' equation. However, for zero BCs, the analysis is not so simple.

16 pages, 3 figures, v4: second solution removed as being unphysical, title modified, paper revised; v5: minor changes

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Cited by in corpus (1)

• Nonuniform Bose-Einstein condensate. II. Doubly coherent states