arXiv subjects
Publications and source records attributed to Daniele Dimonte.
We study a system of $ N $ trapped bosons in the Thomas-Fermi regime with an interacting pair potential of the form $ g_N N^{3β-1} V(N^βx) $, for some $ β\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 $ β\in (0,1/6) $, condensation is preserved by the time evolution.
In this paper we discuss some aspects of fragmented condensation from a mathematical perspective. We first propose a simple way of characterizing finite fragmentation. Then, inspired by recent results of semiclassical analysis applied to bosonic systems with infinitely many degrees of freedom, we address the problem of persistence of fragmented condensation. We show that the latter occurs in interacting systems, in the mean-field regime, and in the limit of large gap of the one-body Hamiltonian.