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Bose–Einstein Condensation in the Luttinger–Sy Model with Contact Interaction

  • Joachim KernerEmail author
  • Maximilian Pechmann
  • Wolfgang Spitzer
Article

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 \(\nu _N\) of the Poisson potential satisfies \([\ln (N)]^4/N^{1 - 2\eta } \ll \nu _N\lesssim 1\) for arbitrary \(0 < \eta \le 1/3\). 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 \(\delta > 0\).

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Joachim Kerner
    • 1
    Email author
  • Maximilian Pechmann
    • 1
  • Wolfgang Spitzer
    • 1
  1. 1.Department of Mathematics and Computer ScienceFernUniversität in HagenHagenGermany

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