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Analysis of Fluctuations Around Non-linear Effective Dynamics

  • Serena CenatiempoEmail author
Chapter
First Online:
Part of the Springer INdAM Series book series (SINDAMS, volume 18)

Abstract

We consider the derivation of effective equations approximating the many-body quantum dynamics of a large system of N bosons in three dimensions, interacting through a two-body potential N3β−1V (N β x). For any 0 ≤ β ≤ 1 well known results establish the trace norm convergence of the k-particle reduced density matrices associated with the solution of the many-body Schrödinger equation towards products of solutions of a one-particle non linear Schrödinger equation, as N → ∞. In collaboration with C. Boccato and B. Schlein we studied fluctuations around the approximate non linear Schrödinger dynamics, obtaining for all 0 < β < 1 a norm approximation of the evolution of an appropriate class of data on the Fock space.

Keywords

Gross-Pitaevskii equation Interacting bosons Nonlinear Schrödinger equations Quantum dynamics Quantum fluctuations 
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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Gran Sasso Science InstituteL’AquilaItaly

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