Effective Evolution Equations from Quantum Dynamics (eBook)

Niels Benedikter, Marcello Porta, Benjamin Schlein (Autoren)

eBook Download: PDF

2015 | 1st ed. 2016
VII, 91 Seiten
Springer International Publishing (Verlag)
978-3-319-24898-1 (ISBN)

Infos

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 (non-equilibrium question) approximating many-body quantum dynamics. The book is divided into seven sections, the first of which briefly reviews the main properties of many-body quantum systems and their time evolution. Section 2 introduces the mean-field regime for bosonic systems and explains how the many-body dynamics can be approximated in this limit using the Hartree equation. Section 3 presents a method, based on the use of coherent states, for rigorously proving the convergence towards the Hartree dynamics, while the fluctuations around the Hartree equation are considered in Section 4. Section 5 focuses on a discussion of a more subtle regime, in which the many-body evolution can be approximated by means of the nonlinear Gross-Pitaevskii equation. Section 6 addresses fermionic systems (characterized by antisymmetric wave functions); here, the fermionic mean-field regime is naturally linked with a semiclassical regime, and it is proven that the evolution of approximate Slater determinants can be approximated using the nonlinear Hartree-Fock equation. In closing, Section 7 reexamines the same fermionic mean-field regime, but with a focus on mixed quasi-free initial data approximating thermal states at positive temperature.           

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 4.11.2015
• Reihe/Serie: SpringerBriefs in Mathematical Physics
• Reihe/Serie: SpringerBriefs in Mathematical Physics
• Reihe/Serie: SpringerBriefs in Physics
• Zusatzinfo: VII, 91 p.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
• Themenwelt: Technik
• Schlagworte: Bosonic Mean-field Regime • Coherent States Approach • Fermionic Mean-field Regime • Gross-Pitaevskii Equation • Hartree Equation • Hartree-Fock Equation • Many-body Quantum Dynamics • Many-body quantum systems • Many-body Schrödinger Dynamics • Many-body Schrödinger Dynamics • Schrödinger Dynamics • Schrödinger Dynamics • Slater Determinants
• ISBN-10: 3-319-24898-7 / 3319248987
• ISBN-13: 978-3-319-24898-1 / 9783319248981