We consider the many-body quantum dynamics of systems of bosons interacting through a two-body potential N^(3b-1)V(N^bx) , scaling with the number of particles N. For b in the interval (0,1) , 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.

Quantum Many-Body Fluctuations Around Nonlinear Schrödinger Dynamics / C. Boccato, S. Cenatiempo, B. Schlein. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - 18:1(2017), pp. 113-191. [10.1007/s00023-016-0513-6]

Quantum Many-Body Fluctuations Around Nonlinear Schrödinger Dynamics

C. Boccato;
2017

Abstract

We consider the many-body quantum dynamics of systems of bosons interacting through a two-body potential N^(3b-1)V(N^bx) , scaling with the number of particles N. For b in the interval (0,1) , 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.
Bose-Einstein condensate; gross-Pitaevskii equation; mean-field approximation; central-limit-theorem; rigorous derivation; interacting boson; excitation spectrum
Settore MAT/07 - Fisica Matematica
20-lug-2016
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/859727
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