Effective Evolution Equations from Quantum Dynamics / / by Niels Benedikter, Marcello Porta, Benjamin Schlein
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| Autore: |
Benedikter Niels
|
| Titolo: |
Effective Evolution Equations from Quantum Dynamics / / by Niels Benedikter, Marcello Porta, Benjamin Schlein
|
| Pubblicazione: | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 |
| Edizione: | 1st ed. 2016. |
| Descrizione fisica: | 1 online resource (97 p.) |
| Disciplina: | 530.12 |
| Soggetto topico: | Quantum theory |
| Mathematical physics | |
| Quantum Physics | |
| Mathematical Physics | |
| Persona (resp. second.): | PortaMarcello |
| SchleinBenjamin | |
| Note generali: | Description based upon print version of record. |
| Nota di bibliografia: | Includes bibliographical references at the end of each chapters. |
| Nota di contenuto: | 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. |
| Sommario/riassunto: | 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. . |
| Titolo autorizzato: | Effective Evolution Equations from Quantum Dynamics |
| ISBN: | 3-319-24898-7 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910254610703321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
SpringerBriefs in Mathematical Physics, . 2197-1757 ; ; 7