# Effective non-linear dynamics of binary condensates and open problems

## TL;DR

This paper discusses the derivation of effective non-linear dynamics for binary Bose-Einstein condensates, focusing on the Gross-Pitaevskii limit, and reviews prior results in the mean field regime.

## Contribution

It provides a rigorous derivation of the coupled non-linear Schrödinger equations for binary condensates in the Gross-Pitaevskii scaling limit, extending previous mean field results.

## Key findings

- Rigorous derivation of coupled non-linear Schrödinger equations
- Analysis of the Gross-Pitaevskii scaling limit
- Comparison with mean field regime results

## Abstract

We report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount of attention in the recent literature in mathematical physics; for such models, the effective dynamics is described by a coupled system of non-linear Sch\"odinger equations. After reviewing and commenting our proof in the mean field regime from a previous paper, we collect the main details needed to obtain the rigorous derivation of the effective dynamics in the Gross-Pitaevskii scaling limit.