Mean-field quantum dynamics for a mixture of Bose-Einstein condensates

TL;DR

This paper proves that in a large quantum system of mixed bosonic species, initial condensation persists over time and the complex many-body dynamics can be effectively described by coupled nonlinear Schrödinger equations.

Contribution

It establishes the persistence of condensation and derives effective coupled nonlinear Schrödinger equations for mixed bosonic systems.

Findings

Condensation persists over time in the system.

Many-body dynamics are well-approximated by coupled nonlinear equations.

Quantitative bounds on the approximation are provided.

Abstract

We study the effective time evolution of a large quantum system consisting of a mixture of different species of identical bosons in interaction. If the system is initially prepared so as to exhibit condensation in each component, we prove that condensation persists at later times and we show quantitatively that the many-body Schr\"{o}dinger dynamics is effectively described by a system of coupled cubic non-linear Schr\"{o}dinger equations, one for each component.