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arXiv · 1701.07755

Analysis of fluctuations around non linear effective dynamics

Serena Cenatiempo
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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 $N^{3β-1}V(N^βx)$. For any $0 \leq β\leq 1$ 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 $N \to \infty$. 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.

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Serena Cenatiempo. 2017-03-12. Analysis of fluctuations around non linear effective dynamics. https://doi.org/10.1007/978-3-319-58904-6_6

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