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

蚀刻术

巡回

细菌等

,Gallbladder Segmentation from 2–D Ultrasound Images Using Active Contour Models and Gradient Vectorows superfluous information which is immaterial in the diagnostic process to be eliminated. In this project, several active contour models were used to segment the shape of the gallbladder, both for cases free of lesions, and for those showing specific disease units, namely: lithiasis, polyps, and a