arXiv:1509.03837 · Annales Henri Poincaré

Quantum Many-Body Fluctuations Around Nonlinear Schrödinger Dynamics

Chiara Boccato, Serena Cenatiempo, Benjamin Schlein

Published Jul 20, 2016• 51 citations

arXiv HTML PDF

DOI: 10.1007/s00023-016-0513-6

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arXiv:1509.03837 · Annales Henri Poincaré

Quantum Many-Body Fluctuations Around Nonlinear Schrödinger Dynamics

Chiara Boccato, Serena Cenatiempo, Benjamin Schlein

Published Jul 20, 2016• 51 citations

arXiv HTML PDF

DOI: 10.1007/s00023-016-0513-6

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

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Fluctuations of

N

-particle quantum dynamics around the nonlinear Schrödinger equation

Abstract We consider a system ofNbosons in the limit

N \rightarrow \infty

N→∞ , interacting through singular potentials. For initial data exhibiting Bose–Einstein condensation, the many-body time evolution is well approximated through a quadratic fluctuation dynamics around a cubic nonlinear Schrödinger equation of the condensate wave function. We show that these fluctuations satisfy a (multi-variate) central limit theorem.