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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Physik & Astronomie Theoretische Physik Effective Evolution Equations from Quantum Dynamics
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Effective Evolution Equations from Quantum Dynamics
Niels Benedikter, Marcello Porta, Benjamin Schlein (Broschiert, Englisch)
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Beschreibung
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. 53,49 €
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Technische Daten
Erscheinungsdatum
14.10.2015
Sprache
Englisch
EAN
9783319248967
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
SpringerBriefs in Mathematical Physics
Sonderedition
Nein
Autor
Niels Benedikter, Marcello Porta, Benjamin Schlein
Seitenanzahl
91
Einbandart
Broschiert
Schlagwörter
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, Schrödinger Dynamics, Slater Determinants
Thema-Inhalt
PHQ - Quantenphysik (Quantenmechanik und Quantenfeldtheorie)
PHU - Mathematische Physik
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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