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1. |
Record Nr. |
UNISA996391019803316 |
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Autore |
Aepinus Johann <1499-1553.> |
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Titolo |
D. Ioannis Aepini liber de purgatorio. Satisfactionibus .. [[electronic resource]] |
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Pubbl/distr/stampa |
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Londini, : [Richard Grafton], Anno.1549 |
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Descrizione fisica |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Printer's name from STC. |
Signatures: A-Zâ´ 2A-2Bâ´ 2Câ¶. |
Reproduction of the original in the British Library. |
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Sommario/riassunto |
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2. |
Record Nr. |
UNINA9910254610703321 |
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Autore |
Benedikter Niels |
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Titolo |
Effective Evolution Equations from Quantum Dynamics / / by Niels Benedikter, Marcello Porta, Benjamin Schlein |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 |
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ISBN |
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Edizione |
[1st ed. 2016.] |
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Descrizione fisica |
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1 online resource (97 p.) |
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Collana |
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SpringerBriefs in Mathematical Physics, , 2197-1757 ; ; 7 |
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Disciplina |
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Soggetti |
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Quantum theory |
Mathematical physics |
Quantum Physics |
Mathematical Physics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references at the end of each chapters. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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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. . |
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