Quantum many-body fluctuations around nonlinear Schrödinger dynamics

We review some results of our paper arXiv:1602.05171v2 on the "nonlinear quasifree approximation" to the many-body Schrödinger dynamics of Bose gases. In that paper, we derive, with the help of this approximation, the time-dependent Hartree-Fock-Bogoliubov (HFB) equations, providing an approximate description of the dynamics of quantum fluctuations around a Bose-Einstein condensate and study properties of these equations.

arXiv:1805.04689May 12, 20180 citations

Central limit theorem for Bose gases interacting through singular potentials

Simone Rademacher

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.

arXiv:1908.11672Letters in Mathematical PhysicsMar 12, 202015 citations

Quantum many-body fluctuations around nonlinear Schrödinger dynamics

Chiara Boccato, Serena Cenatiempo, Benjamin Schlein

Published Jan 31, 2017• 58 citations

Publisher

DOI: 10.5167/uzh-137401

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Central limit theorem for Bose gases interacting through singular potentials

Simone Rademacher

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.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.

arXiv:1908.11672Letters in Mathematical PhysicsMar 12, 202015 citations

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.