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المواصفات
| الناشر | Springer |
| رقم الكتاب المعياري الدولي 13 | 9783319248967 |
| رقم الكتاب المعياري الدولي 10 | 3319248960 |
| اللغة | الإنجليزية |
| العنوان الفرعي للكتاب | Springerbriefs In Mathematical Physics |
| وصف الكتاب | 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. |
| رقم الطبعة | 1st edition |
| تاريخ النشر | 14-Oct-15 |
| عدد الصفحات | 100 |
Effective Evolution Equations From Quantum Dynamics Paperback English by Niels Benedikter - 14-Oct-15
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