# Dynamics of Bose-Einstein Condensates

## TL;DR

This paper reviews recent rigorous derivations of the Gross-Pitaevskii equation from many-body quantum dynamics, elucidating the behavior of Bose-Einstein condensates over time.

## Contribution

It provides a rigorous mathematical derivation of the nonlinear Schrödinger equation governing Bose-Einstein condensate dynamics from many-body quantum physics.

## Key findings

- Derivation of the Gross-Pitaevskii equation from first principles
- Validation of the nonlinear Schrödinger equation as a model for condensate dynamics
- Clarification of the connection between microscopic quantum mechanics and macroscopic condensate behavior

## Abstract

We report on some recent results concerning the dynamics of Bose-Einstein condensates, obtained in a series of joint papers with L. Erdos and H.-T. Yau. Starting from many body quantum dynamics, we present a rigorous derivation of a cubic nonlinear Schroedinger equation known as the Gross-Pitaevskii equation for the time evolution of the condensate wave function.