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20170520152634.0 |
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|a 9783319248981
|9 978-3-319-24898-1
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|a 10.1007/978-3-319-24898-1
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|a QC173.96-174.52
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|a 530.12
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|a Benedikter, Niels.
|e author.
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|a Effective Evolution Equations from Quantum Dynamics
|h [electronic resource] /
|c by Niels Benedikter, Marcello Porta, Benjamin Schlein.
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|a Cham :
|b Springer International Publishing :
|b Imprint: Springer,
|c 2016.
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|a VII, 91 p.
|b online resource.
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|a text
|b txt
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|a computer
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|a online resource
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|a text file
|b PDF
|2 rda
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|a SpringerBriefs in Mathematical Physics,
|x 2197-1757 ;
|v 7
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|a 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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|a 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. .
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|a Physics.
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|a Mathematical physics.
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|a Quantum physics.
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|a Physics.
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|a Quantum Physics.
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|a Mathematical Physics.
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|a Porta, Marcello.
|e author.
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|a Schlein, Benjamin.
|e author.
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783319248967
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| 830 |
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|a SpringerBriefs in Mathematical Physics,
|x 2197-1757 ;
|v 7
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|u http://dx.doi.org/10.1007/978-3-319-24898-1
|z Full Text via HEAL-Link
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|a ZDB-2-PHA
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|a Physics and Astronomy (Springer-11651)
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