Analysis of fluctuations around non linear effective dynamics

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 $N^{3\beta -1}V(N^{\beta }x)$. For any $0\le \beta \le 1$ 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 $0<\beta <1$ a norm approximation of the evolution of an appropriate class of data on the Fock space.

18 pages; contribution to the Proceedings of the INdAM meeting "Contemporary Trends in the Mathematics of Quantum Mechanics" held in Rome in July 2016

References in corpus (1)

• Geometric methods for nonlinear many-body quantum systems

Cited by in corpus (1)

• Convergence rate towards the fractional Hartree-equation with singular potentials in higher Sobolev norms