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arXiv · 1710.09743

Fluctuations of $N$-particle quantum dynamics around the nonlinear Schrödinger equation

Christian Brennecke·Phan Thành Nam·Marcin Napiórkowski·Benjamin Schlein
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Abstract

We consider a system of $N$ bosons interacting through a singular two-body potential scaling with $N$ and having the form $N^{3β-1} V (N^βx)$, for an arbitrary parameter $β\in (0,1)$. We provide a norm-approximation for the many-body evolution of initial data exhibiting Bose-Einstein condensation in terms of a cubic nonlinear Schrödinger equation for the condensate wave function and of a unitary Fock space evolution with a generator quadratic in creation and annihilation operators for the fluctuations.

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Christian Brennecke, Phan Thành Nam, Marcin Napiórkowski, Benjamin Schlein. 2018-10-24. Fluctuations of $N$-particle quantum dynamics around the nonlinear Schrödinger equation. https://arxiv.org/abs/1710.09743

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