{"product_id":"9783319248967","title":"SpringerBriefs in Mathematical Physics","description":"\u003ch1\u003eSpringerBriefs in Mathematical Physics\u003c\/h1\u003e \u003ch2\u003eBenedikter, Niels; Porta, Marcello; Schlein, Benjamin\u003c\/h2\u003e \u003cp\u003eThese 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.           \u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2015-10-14\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783319248967\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-319-24898-1\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 91\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":47409842946188,"sku":"9783319248967","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783319248967.jpg?v=1775835672","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783319248967","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}