On Bose–Einstein Condensation in the Luttinger–Sy Model with Finite Interaction Strength

  • Joachim Kerner
  • Maximilian Pechmann
  • Wolfgang SpitzerEmail author


We study Bose–Einstein condensation (BEC) in the Luttinger–Sy model. Here, Bose point particles in one spatial dimension do not interact with each other, but, through a positive (repulsive) point potential with impurities which are randomly located along the real line according to the points of a Poisson process. Our emphasis is on the case in which the interaction strength is not infinite. As a main result, we prove that in thermal equilibrium the one-particle ground state is macroscopically occupied, provided that the particle density is larger than a critical one depending on the temperature.


Bose–Einstein condensation Luttinger–Sy model Lifshitz tails 



It is our pleasure to thank Werner Kirsch and Hajo Leschke for interesting discussions and useful remarks that led to an improvement of the manuscript.


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Authors and Affiliations

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

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