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Journal of Low Temperature Physics

, Volume 182, Issue 5–6, pp 170–184 | Cite as

Bose–Einstein Condensation in a One-Dimensional System of Interacting Bosons

  • Maksim TomchenkoEmail author
Article

Abstract

Using the Vakarchuk formulae for the density matrix, we calculate the number \(N_{k}\) of atoms with momentum \(\hbar k\) for the ground state of a uniform one-dimensional periodic system of interacting bosons. We obtain for impenetrable point bosons \( N_{0} \approx 2\sqrt{N}\) and \(N_{k=2\pi j/L} \simeq 0.31~N_{0}/\sqrt{|j|}\). That is, there is no condensate or quasicondensate on low levels at large N. For almost point bosons with weak coupling (\(\beta =\frac{\nu _{0}m}{\pi ^{2}\hbar ^{2}n} \ll 1\)), we obtain \(\frac{N_{0}}{N} \approx \left( \frac{2}{N\sqrt{\beta }}\right) ^{\sqrt{\beta }/2} \) and \( N_{k=2\pi j/L} \approx \frac{N_{0}\sqrt{\beta }}{4|j|^{1-\sqrt{\beta }/2}}\). In this case, the quasicondensate exists on the level with \(k=0\) and on low levels with \(k\ne 0\), if N is large and \( \beta \) is small (e.g., for \(N \sim 10^{10} \), \( \beta \sim 0.01\)). A method of measurement of such fragmented quasicondensate is proposed.

Keywords

Quasicondensate Low dimensions Interacting bosons 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Bogolyubov Institute for Theoretical PhysicsKievUkraine

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