On Bose-Einstein condensates in the Thomas-Fermi regime

Abstract

We study a system of $N$ trapped bosons in the Thomas-Fermi regime with an interacting pair potential of the form $g_N{N}^{3\beta -1}V(N^{\beta }x)$, for some $\beta \in (0,1/3)$ and $g_N$ diverging as $N\to \infty$. We prove that there is complete Bose-Einstein condensation at the level of the ground state and, furthermore, that, if $\beta \in (0,1/6)$, condensation is preserved by the time evolution.

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Cited by in corpus (5)

• Bose-Einstein condensation on hyperbolic spaces
• Uniform in Time Convergence to Bose-Einstein Condensation for a Weakly Interacting Bose Gas with an External Potential
• The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime
• A second order upper bound on the ground state energy of a Bose gas beyond the Gross-Pitaevskii regime
• Reduced fluctuations for bosons in a double well