# Probability and Stochastics Seminar

TITLE: On Bose-Einstein condensation in the Luttinger-Sy model with contact interaction, Part 2

SPEAKER: Maximilian Pechmann, UTK

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 $\nu_N N^{3/5+\delta}$ for $\delta > 0$.

Tuesday, March 3, 2020 at 2:10pm to 3:00pm

Ayres Hall, 111

Department
Mathematics
Contact Name

Rosinski

Contact Email

jrosinsk@utk.edu

Contact Phone

865-974-2461

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