00981nam0-2200325---450-99000817406040332120050802111348.01-4020-1457-0000817406FED01000817406(Aleph)000817406FED0100081740620050802d2003----km-y0itay50------baengNE--------001yySingular differential and integral equations with applicationsby Ravi P. Agarwal and Donal O'ReganDordrechtKluwer Academic2003xi, 402 p.ill.25 cmEquazioni differenziali515.35Agarwal,Ravi P.41786O'Regan,Donald382738ITUNINARICAUNIMARCBK99000817406040332110 B I 582DIEL 3373DINELDINELSingular differential and integral equations with applications736102UNINA04142nam 22006375 450 991025461070332120200705030327.03-319-24898-710.1007/978-3-319-24898-1(CKB)3710000000486781(EBL)4068161(SSID)ssj0001585064(PQKBManifestationID)16265532(PQKBTitleCode)TC0001585064(PQKBWorkID)14866007(PQKB)10677091(DE-He213)978-3-319-24898-1(MiAaPQ)EBC4068161(PPN)190526629(EXLCZ)99371000000048678120151006d2016 u| 0engur|n|---|||||txtccrEffective Evolution Equations from Quantum Dynamics /by Niels Benedikter, Marcello Porta, Benjamin Schlein1st ed. 2016.Cham :Springer International Publishing :Imprint: Springer,2016.1 online resource (97 p.)SpringerBriefs in Mathematical Physics,2197-1757 ;7Description based upon print version of record.3-319-24896-0 Includes bibliographical references at the end of each chapters.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.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. .SpringerBriefs in Mathematical Physics,2197-1757 ;7Quantum theoryMathematical physicsQuantum Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19080Mathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Quantum theory.Mathematical physics.Quantum Physics.Mathematical Physics.530.12Benedikter Nielsauthttp://id.loc.gov/vocabulary/relators/aut748776Porta Marcelloauthttp://id.loc.gov/vocabulary/relators/autSchlein Benjaminauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910254610703321Effective Evolution Equations from Quantum Dynamics2522517UNINA