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We consider a system of N bosons interacting through a singular two-body potential scaling with N and having the form , for an arbitrary parameter . 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, Fluctuations of N-particle quantum dynamics around the nonlinear Schrödinger equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 5, pp. 1201–1235DOI 10.1016/J.ANIHPC.2018.10.007