Bose--Einstein condensation in the Luttinger--Sy model with contact interaction
| Autor: | Kerner, Joachim, Pechmann, Maximilian, Spitzer, Wolfgang |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Annales Henri Poincar\'e (2019) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00023-019-00771-w |
| Popis: | 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 $\nu_N$ of the Poisson potential satisfies $[\ln (N)]^4/N^{1 - 2\eta} \ll \nu_N \lesssim 1$ for arbitrary $0 < \eta \leq 1/3$. 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 $0 < \eta < 1/6$ we prove that the mean particle density in the largest interval is almost surely bounded asymptotically by $\nu_NN^{3/5+\delta}$ for $\delta > 0$. Comment: 35 pages |
| Databáze: | arXiv |
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