| 书目名称 | Effective Evolution Equations from Quantum Dynamics |
| 编辑 | Niels Benedikter,Marcello Porta,Benjamin Schlein |
| 视频video | |
| 概述 | Includes supplementary material: |
| 丛书名称 | SpringerBriefs in Mathematical Physics |
| 图书封面 |  |
| 描述 | 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 |
| 出版日期 | Book 2016 |
| 关键词 | Bosonic Mean-field Regime; Coherent States Approach; Fermionic Mean-field Regime; Gross-Pitaevskii Equa |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-319-24898-1 |
| isbn_softcover | 978-3-319-24896-7 |
| isbn_ebook | 978-3-319-24898-1Series ISSN 2197-1757 Series E-ISSN 2197-1765 |
| issn_series | 2197-1757 |
| copyright | The Author(s) 2016 |
发表于 2025-3-21 19:07:24
