Local enhancement of the mean-field approximation for bosons

2024/12/18 by Lemm, Marius, Rademacher, Simone, Zhang, Jingxuan
#35Q40 #35Q55 #81V70 #81V73 #82C10 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2412.13868

Abstract

We study the quantum many-body dynamics of a Bose-Einstein condensate (BEC) on the lattice in the mean-field regime. We derive a local enhancement of the mean-field approximation: At positive distance ρ>0 from the initial BEC, the mean-field approximation error at time t≤ ρ/v is bounded as ρ^-n, for arbitrarily large n≥ 1. This is a consequence of new ballistic propagation bounds on the fluctuations around the condensate. To prove this, we develop a variant of the ASTLO (adiabatic spacetime localization observable) method for the particle non-conserving generator of the fluctuation dynamics around Hartree states.

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