東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Effective evolution equations from q...

Benedikter, Niels.

Linked to FindBook

Google Book

Amazon

博客來

Effective evolution equations from quantum dynamics

Record Type:	Electronic resources : Monograph/item
Title/Author:	Effective evolution equations from quantum dynamics/ by 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.
[NT 15003449]:	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.
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:

516552
Quantum theory.

LC Class. No.: QC174.12

Dewey Class. No.: 530.12

Effective evolution equations from quantum dynamics
LDR:02887nmm a2200325 a 4500 001 2029522
003 DE-He213
005 20160801162046.0
006 m d
007 cr nn 008maaau
008 160908s2016 gw s 0 eng d
020 $a 9783319248981$q(electronic bk.)
020 $a 9783319248967$q(paper)
024 7 $a 10.1007/978-3-319-24898-1 $2 doi
035 $a 978-3-319-24898-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QC174.12
072 7 $a PHQ $2 bicssc
072 7 $a SCI057000 $2 bisacsh
082 0 4 $a 530.12 $2 23
090 $a QC174.12 $b .B463 2016
100 1 $a Benedikter, Niels. $3 2180582
245 1 0 $a Effective evolution equations from quantum dynamics $h [electronic resource] / $c by Niels Benedikter, Marcello Porta, Benjamin Schlein.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a vii, 91 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematical physics, $x 2197-1757 ; $v v.7
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.
650 0 $a Quantum theory. $3 516552
650 0 $a Mathematical physics. $3 516853
650 1 4 $a Physics. $3 516296
650 2 4 $a Quantum Physics. $3 893952
650 2 4 $a Mathematical Physics. $3 1542352
700 1 $a Porta, Marcello. $3 2180583
700 1 $a Schlein, Benjamin. $3 2180584
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in mathematical physics ; $v v.1. $3 2072051
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-24898-1
950 $a Physics and Astronomy (Springer-11651)