Effective evolution equations from quantum dynamics
74,69 $

Effective evolution equations from quantum dynamics

NIELS BENEDIKTER, MARCELLO PORTA, SCHL


Effective evolution equations from quantum dynamics

NIELS BENEDIKTER, MARCELLO PORTA, SCHL

74,69 $ 74,69 $
Régulier: 74,69 $
Rabais: 0,00 $ (0%)
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Résumé
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.           
Détails
Titre
Effective evolution equations from quantum dynamics
Prix
74,69 $
Sujet
Format Poche
Non
Langue
Français/French
Date de publication
2015-11-04
ISBN
9783319248981
Code Interne
2171227
Numéro de produit
2171227
Format numérique
pdf
Disponibilité
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Protection
Adobe DRM
Entrepôt Numérique
NUMILOG

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