Quantum many-body fluctuations around nonlinear Schr\"odinger dynamics

TL;DR

This paper studies the quantum dynamics of many-boson systems with scaled interactions, providing a norm-approximation of the evolution and introducing a fluctuation dynamics correction to the nonlinear Schrödinger equation.

Contribution

It introduces a novel fluctuation dynamics approach to approximate many-body quantum evolution for bosons with specific interaction scaling.

Findings

Achieved a norm-approximation of the quantum evolution.

Developed a fluctuation dynamics governed by a quadratic generator.

Extended understanding of many-body bosonic systems with scaled interactions.

Abstract

We consider the many body quantum dynamics of systems of bosons interacting through a two-body potential $N^{3\beta-1} V (N^\beta x)$, scaling with the number of particles $N$. For $0< \beta < 1$, 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 Schr\"odinger equation by means of a fluctuation dynamics, governed by a quadratic generator.