A note on the validity of Bogoliubov correction to mean-field dynamics

2016/04/18 by Nam, Phan Thành, Napiórkowski, Marcin · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1604.05240

Abstract

We study the norm approximation to the Schrödinger dynamics of N bosons in ℝ³ with an interaction potential of the form N^3β-1w(N^β(x-y)). Assuming that in the initial state the particles outside of the condensate form a quasi-free state with finite kinetic energy, we show that in the large N limit, the fluctuations around the condensate can be effectively described using Bogoliubov approximation for all 0≤ β<1/2. The range of β is expected to be optimal for this large class of initial states.

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