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arXiv · 1804.07697

Bose--Einstein condensation in the Luttinger--Sy model with contact interaction

Joachim Kerner·Maximilian Pechmann·Wolfgang Spitzer
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Abstract

We study bosons on the real line in a Poisson random potential (Luttinger--Sy model) with contact interaction in the thermodynamic limit at absolute zero temperature. We prove that generalized Bose--Einstein condensation (BEC) occurs almost surely if the intensity $ν_N$ of the Poisson potential satisfies $[\ln (N)]^4/N^{1 - 2η} \ll ν_N \lesssim 1$ for arbitrary $0 < η\leq 1/3$. We also show that the contact interaction alters the type of condensation, going from a type-I BEC to a type-III BEC as the strength of this interaction is increased. Furthermore, for sufficiently strong contact interactions and $0 < η< 1/6$ we prove that the mean particle density in the largest interval is almost surely bounded asymptotically by $ν_NN^{3/5+δ}$ for $δ> 0$.

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Joachim Kerner, Maximilian Pechmann, Wolfgang Spitzer. 2018-04-20. Bose--Einstein condensation in the Luttinger--Sy model with contact interaction. https://doi.org/10.1007/s00023-019-00771-w

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