SpringerBriefs in Mathematical Physics

Effective Evolution Equations from Quantum Dynamics

Authors: Benedikter, Niels, Porta, Marcello, Schlein, Benjamin

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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.           

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook 44,02 €
price for Italia (gross)
  • ISBN 978-3-319-24898-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 57,19 €
price for Italia (gross)
  • ISBN 978-3-319-24896-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Effective Evolution Equations from Quantum Dynamics
Authors
Series Title
SpringerBriefs in Mathematical Physics
Series Volume
7
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-24898-1
DOI
10.1007/978-3-319-24898-1
Softcover ISBN
978-3-319-24896-7
Series ISSN
2197-1757
Edition Number
1
Number of Pages
VII, 91
Topics