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.
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