Large Deviations for the Ground State of Weakly Interacting Bose Gases

Rademacher, Simone (2. Juli 2024): Large Deviations for the Ground State of Weakly Interacting Bose Gases. In: Annales Henri Poincaré, Bd. 26: S. 1239-1289

Abstract

We consider the ground state of a Bose gas of N particles on the three-dimensional unit torus in the mean-field regime that is known to exhibit Bose–Einstein condensation. Bounded one-particle operators with law given through the interacting Bose gas’ ground state correspond to dependent random variables due to the bosons’ correlation. We prove that in the limit N -> Infinity bounded one-particle operators with law given by the ground state satisfy large deviation estimates. We derive a lower and an upper bound on the rate function that match up to second order and that are characterized by quantum fluctuations around the condensate.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1424-0637
• Sprache: Englisch