Dispersion law for a one-dimensional weakly interacting Bose gas with zero boundary conditions
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arXiv
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| Format: | Preprint |
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2012
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| _version_ | 1866911975338934272 |
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| author | Tomchenko, Maksim |
| author_facet | Tomchenko, Maksim |
| contents | 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 $E_{B}(k) = \sqrt{\left (\frac{\hbar^{2} k^2}{2m}\right )^{2} + n_{0}ν(k)\frac{\hbar^2 k^2}{m}}$. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1211_1723 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Dispersion law for a one-dimensional weakly interacting Bose gas with zero boundary conditions Tomchenko, Maksim Quantum Gases 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 $E_{B}(k) = \sqrt{\left (\frac{\hbar^{2} k^2}{2m}\right )^{2} + n_{0}ν(k)\frac{\hbar^2 k^2}{m}}$. 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. |
| title | Dispersion law for a one-dimensional weakly interacting Bose gas with zero boundary conditions |
| topic | Quantum Gases |
| url | https://arxiv.org/abs/1211.1723 |