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Quantum Many-Body Fluctuations Around Nonlinear Schrödinger Dynamics

Abstract

We consider the many-body quantum dynamics of systems of bosons interacting through a two-body potential \({N^{3\beta-1} V (N^\beta x)}\), scaling with the number of particles N. For \({0 < \beta < 1}\), we obtain a norm-approximation of the evolution of an appropriate class of data on the Fock space. To this end, we need to correct the evolution of the condensate described by the one-particle nonlinear Schrödinger equation by means of a fluctuation dynamics, governed by a quadratic generator.

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Boccato, C., Cenatiempo, S. & Schlein, B. Quantum Many-Body Fluctuations Around Nonlinear Schrödinger Dynamics. Ann. Henri Poincaré 18, 113–191 (2017). https://doi.org/10.1007/s00023-016-0513-6

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  • DOI: https://doi.org/10.1007/s00023-016-0513-6