| 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. |
استرجاع مجاني وسهل
أفضل العروض
![/fashion-men/jack_jones/?sort[by]=popularity&sort[dir]=desc&limit=50](https://a.nooncdn.com/cms/pages/20240305/4ef48af441e2b44cea1673cd2e4aff67/en_dk-men-brands-04.png)
![/fashion-men/seventy_five/?sort[by]=popularity&sort[dir]=desc&limit=50](https://a.nooncdn.com/cms/pages/20240305/4ef48af441e2b44cea1673cd2e4aff67/en_dk-womens-new-brands-01.png)
![/fashion-men/skechers/?sort[by]=popularity&sort[dir]=desc&limit=50](https://a.nooncdn.com/cms/pages/20240305/4ef48af441e2b44cea1673cd2e4aff67/en_dk-womens-new-brands-02.png)
![/fashion-women/mango/?sort[by]=popularity&sort[dir]=desc&limit=50](https://a.nooncdn.com/cms/pages/20240305/4ef48af441e2b44cea1673cd2e4aff67/en_dk-women-brands-05.png)
![/fashion-women/guess/?sort[by]=popularity&sort[dir]=desc&limit=50](https://a.nooncdn.com/cms/pages/20240305/4ef48af441e2b44cea1673cd2e4aff67/en_dk-women-brands-09.png)
![/fashion-women/ella/?sort[by]=popularity&sort[dir]=desc&limit=50](https://a.nooncdn.com/cms/pages/20241812/en_dk-nav-brands-01.png)
![/fashion-women/skechers/?sort[by]=popularity&sort[dir]=desc&limit=50](https://a.nooncdn.com/cms/pages/20241812/en_dk-nav-brands-02.png)
![/fashion/view-all-kids-clothing/nike/?sort[by]=popularity&sort[dir]=desc&limit=50](https://a.nooncdn.com/cms/pages/20240911/nav-web/en_mb_uae_brand-01.png)
![/fashion/view-all-kids-clothing/disney/disney_minnie_mouse/disney_frozen/disney_princess/disney_mickey_mouse/disney_baby/?sort[by]=popularity&sort[dir]=desc&limit=50](https://a.nooncdn.com/cms/pages/20240911/nav-web/en_mb_uae_brand-03.png)
![/fashion/view-all-kids-clothing/new_balance/?sort[by]=popularity&sort[dir]=desc&limit=50](https://a.nooncdn.com/cms/pages/20240911/nav-web/en_mb_uae_brand-11.png)
![/music-movies-and-tv-shows/musical-instruments-24670/pianos-keyboards-synthesizers/chloris/?sort[by]=popularity&sort[dir]=desc&limit=50&page=1&isCarouselView=false](https://f.nooncdn.com/cms/pages/20250407/books-nav/en_uae_dk-nav-brands-04.png)
![/music-movies-and-tv-shows/musical-instruments-24670/pianos-keyboards-synthesizers/roland/?sort[by]=popularity&sort[dir]=desc&limit=50&page=1&isCarouselView=false](https://f.nooncdn.com/cms/pages/20250407/books-nav/en_uae_dk-nav-brands-05.png)
![/music-movies-and-tv-shows/musical-instruments-24670/pianos-keyboards-synthesizers/donner/?sort[by]=popularity&sort[dir]=desc&limit=50&page=1&isCarouselView=false](https://f.nooncdn.com/cms/pages/20250407/books-nav/en_uae_dk-nav-brands-06.png)
![/music-movies-and-tv-shows/musical-instruments-24670/pianos-keyboards-synthesizers/korg/?sort[by]=popularity&sort[dir]=desc&limit=50&page=1&isCarouselView=false](https://f.nooncdn.com/cms/pages/20250407/books-nav/en_uae_dk-nav-brands-07.png)
