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Effective evolution equations from q...

Benedikter, Niels.

Effective evolution equations from quantum dynamics

Record Type:	Electronic resources : Monograph/item
Title/Author:	Effective evolution equations from quantum dynamicsby Niels Benedikter, Marcello Porta, Benjamin Schlein.
Author:	Benedikter, Niels.
other author:	Porta, Marcello.
Published:	Cham :Springer International Publishing :2016.
Description:	vii, 91 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Quantum theory.
Online resource:	http://dx.doi.org/10.1007/978-3-319-24898-1
ISBN:	9783319248981$q(electronic bk.)

Effective evolution equations from quantum dynamics
Benedikter, Niels.

Effective evolution equations from quantum dynamics[electronic resource] /by Niels Benedikter, Marcello Porta, Benjamin Schlein. - Cham :Springer International Publishing :2016. - vii, 91 p. :ill., digital ;24 cm. - SpringerBriefs in mathematical physics,v.72197-1757 ;. - SpringerBriefs in mathematical physics ;v.1..

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.

These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrodinger 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.

ISBN: 9783319248981$q(electronic bk.)

Standard No.: 10.1007/978-3-319-24898-1doiSubjects--Topical Terms:

199020
Quantum theory.

LC Class. No.: QC174.12

Dewey Class. No.: 530.12

Effective evolution equations from quantum dynamics
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505 0 $a 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.
520 $a These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrodinger 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.
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