Effective evolution equations from many body quantum dynamics
Benjamin Schlein
TL;DR
This paper reviews recent advances in deriving simplified effective equations from fundamental quantum many-body dynamics, focusing on applications to boson stars and Bose-Einstein condensates.
Contribution
It presents new derivations of the semi-relativistic Hartree and Gross-Pitaevskii equations from first principles quantum dynamics.
Findings
Derivation of the semi-relativistic Hartree equation for boson stars
Derivation of the Gross-Pitaevskii equation for Bose-Einstein condensates
Clarification of the connection between microscopic quantum models and macroscopic effective equations
Abstract
In these notes we review some recent results concerning the derivation of effective equations from first principle quantum dynamics. In particular, we discuss the derivation of the semi-relativistic Hartree equation for the evolution of boson stars, and the derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensates.
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Taxonomy
TopicsCold Atom Physics and Bose-Einstein Condensates · Advanced Mathematical Physics Problems · Quantum, superfluid, helium dynamics