Cargando…
Effective Evolution Equations from Quantum Dynamics
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 (...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2016.
|
| Edición: | 1st ed. 2016. |
| Colección: | SpringerBriefs in Mathematical Physics,
7 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-3-319-24898-1 | ||
| 003 | DE-He213 | ||
| 005 | 20220119194534.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 151006s2016 sz | s |||| 0|eng d | ||
| 020 | |a 9783319248981 |9 978-3-319-24898-1 | ||
| 024 | 7 | |a 10.1007/978-3-319-24898-1 |2 doi | |
| 050 | 4 | |a QC173.96-174.52 | |
| 072 | 7 | |a PHQ |2 bicssc | |
| 072 | 7 | |a SCI057000 |2 bisacsh | |
| 072 | 7 | |a PHQ |2 thema | |
| 082 | 0 | 4 | |a 530.12 |2 23 |
| 100 | 1 | |a Benedikter, Niels. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Effective Evolution Equations from Quantum Dynamics |h [electronic resource] / |c by Niels Benedikter, Marcello Porta, Benjamin Schlein. |
| 250 | |a 1st ed. 2016. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2016. | |
| 300 | |a VII, 91 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a SpringerBriefs in Mathematical Physics, |x 2197-1765 ; |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 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. . | ||
| 650 | 0 | |a Quantum physics. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 1 | 4 | |a Quantum Physics. |
| 650 | 2 | 4 | |a Mathematical Physics. |
| 700 | 1 | |a Porta, Marcello. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Schlein, Benjamin. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319248967 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319248974 |
| 830 | 0 | |a SpringerBriefs in Mathematical Physics, |x 2197-1765 ; |v 7 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-319-24898-1 |z Texto Completo |
| 912 | |a ZDB-2-PHA | ||
| 912 | |a ZDB-2-SXP | ||
| 950 | |a Physics and Astronomy (SpringerNature-11651) | ||
| 950 | |a Physics and Astronomy (R0) (SpringerNature-43715) | ||