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Dispersion Law for a One-Dimensional Weakly Interacting Bose Gas with Zero Boundary Conditions

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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 Bogoliubov law \(E_{B}(k) = \sqrt{\left( \frac{\hbar ^{2} k^2}{2\,m}\right) ^{2} + n_{0}\nu (k)\frac{\hbar ^2 k^2}{m}}\). 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.

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Acknowledgements

The author is grateful to Yu. Shtanov for discussions. This research was supported by the National Academy of Sciences of Ukraine (Project No. 0123U102283) and the Simons Foundation.

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  1. Bogolyubov Institute for Theoretical Physics, 14b, Metrolohichna Str., Kyiv, 03143, Ukraine

    Maksim Tomchenko

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Tomchenko, M. Dispersion Law for a One-Dimensional Weakly Interacting Bose Gas with Zero Boundary Conditions. J Low Temp Phys (2024). https://doi.org/10.1007/s10909-024-03136-8

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