Effective Evolution Equations from Quantum Dynamics
Niels Benedikter, Marcello Porta, Benjamin Schlein
TL;DR
This paper reviews the derivation of effective equations that approximate the complex quantum many-body dynamics, providing rigorous mathematical foundations for simplifying quantum evolution models.
Contribution
It offers a comprehensive review of methods to rigorously derive effective evolution equations from quantum many-body dynamics.
Findings
Derivation of effective equations from quantum dynamics
Mathematical rigor in quantum evolution approximations
Application to physically relevant regimes
Abstract
In these notes we review the material presented at the summer school on "Mathematical Physics, Analysis and Stochastics" held at the University of Heidelberg in July 2014. We consider the time-evolution of quantum systems and in particular the rigorous derivation of effective equations approximating the many-body Schr\"odinger dynamics in certain physically interesting regimes.
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