Derivation of effective evolution equations from many body quantum dynamics

TL;DR

This paper reviews recent progress in deriving simplified effective evolution equations, like the Hartree and Gross-Pitaevskii equations, from the fundamental quantum dynamics of many-body systems.

Contribution

It provides a comprehensive overview of the derivation methods for mean field and Bose-Einstein condensate equations from first principles.

Findings

Derivation of the Hartree equation for mean field systems.

Derivation of the Gross-Pitaevskii equation for Bose-Einstein condensates.

Clarification of the connection between quantum many-body dynamics and effective equations.

Abstract

We review some recent results concerning the derivation of effective evolution equations from first principle quantum dynamics. In particular, we discuss the derivation of the Hartree equation for mean field systems and the derivation of the Gross-Pitaevskii equation for the time evolution of Bose-Einstein condensates.