Titlebook: Effective Evolution Equations from Quantum Dynamics; Niels Benedikter,Marcello Porta,Benjamin Schlein Book 2016 The Author(s) 2016 Bosonic

FELON

Fluctuations Around Hartree Dynamics,We introduce Bogoliubov transformations. These allow us to describe the quantum fluctuations around the mean-field limit. We also discuss the probabilistic interpretation in terms of a central limit theorem.

DECRY

The Gross-Pitaevskii Regime,he differences to the mean-field regime. We then present two ways of deriving the time-dependent Gross-Pitaevskii equation from the many-body dynamics: using the BBGKY hierarchy or using squeezed coherent states (in other words, Bogoliubov transformations).

光滑

Mean-Field Regime for Fermionic Systems,led to a semi-classical limit. We explain this fact in detail and then introduce Hartree-Fock theory, with some comments on the relation to Thomas-Fermi theory and the Vlasov equation. We introduce particle-hole transformations and derive the Hartree-Fock equation by a method analogous to the bosoni

媒介

Dynamics of Fermionic Quasi-Free Mixed States,in the Hilbert space anymore. However, the Araki-Wyss representation allows us to describe it by a vector in a ‘doubled’ Hilbert space. We use the Araki-Wyss method to derive the time-dependent Hartree-Fock equation for mixed states.

娘娘腔

Book 2016ction 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

maudtin

Effective Evolution Equations from Quantum Dynamics

faddish

2197-1757 ed 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 naturally978-3-319-24896-7978-3-319-24898-1Series ISSN 2197-1757 Series E-ISSN 2197-1765

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