bokomslag Effective Evolution Equations from Quantum Dynamics
Vetenskap & teknik

Effective Evolution Equations from Quantum Dynamics

Niels Benedikter Marcello Porta Benjamin Schlein

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  • 91 sidor
  • 2015
These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrdinger 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.
  • Författare: Niels Benedikter, Marcello Porta, Benjamin Schlein
  • Illustratör: Bibliographie
  • Format: Pocket/Paperback
  • ISBN: 9783319248967
  • Språk: Engelska
  • Antal sidor: 91
  • Utgivningsdatum: 2015-10-14
  • Förlag: Springer International Publishing AG