Effective Evolution Equations from Quantum Dynamics

• Main Authors: Benedikter, Niels (Author), Porta, Marcello (Author), Schlein, Benjamin (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: SpringerBriefs in Mathematical Physics, 7
• Subjects: Physics.; Mathematical physics.; Quantum physics.; Quantum Physics.; Mathematical Physics.

These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrödinger dynamics in certain physically interesting regimes. The focus is primarily on the derivation of time-dependent effective theories (n...

Table of Contents:

• Introduction
• Mean-Field Regime for Bosonic Systems
• Coherent States Approach.-Fluctuations Around Hartree Dynamics
• The Gross-Pitaevskii Regime
• Mean-Field regime for Fermionic Systems
• Dynamics of Fermionic Quasi-Free Mixed States
• The Role of Correlations in the Gross-Pitaevskii Energy.