In this Thesis we discuss the Bose-Einstein condensation (BEC) in the Thomas-Fermi limit for a many-body system, both in the stationary and in the dynamical framework. In particular, we prove that if the pair interaction is of the form $ g_N N^{3beta-1}(N^beta x) $, with $ g_N $ growing as $ N $ goes to infinity and $ beta $ smaller than 1/3 there is BEC in the ground state of a system in a box. We also prove that in a trapped system, if there is BEC in the initial datum, BEC is preserved, at least for $ beta $ smaller than 1/6.

Mathematics of the Bose Gas in the Thomas-Fermi Regime / Dimonte, Daniele. - (2019 Sep 27).

Mathematics of the Bose Gas in the Thomas-Fermi Regime

Dimonte, Daniele
2019

Abstract

In this Thesis we discuss the Bose-Einstein condensation (BEC) in the Thomas-Fermi limit for a many-body system, both in the stationary and in the dynamical framework. In particular, we prove that if the pair interaction is of the form $ g_N N^{3beta-1}(N^beta x) $, with $ g_N $ growing as $ N $ goes to infinity and $ beta $ smaller than 1/3 there is BEC in the ground state of a system in a box. We also prove that in a trapped system, if there is BEC in the initial datum, BEC is preserved, at least for $ beta $ smaller than 1/6.
Correggi, Michele
Dimonte, Daniele
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/103200
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