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Effective Evolution Equations from Quantum Dynamics (SpringerBriefs in Mathematical Physics, 7) by Niels Benedikter, Marcello Porta, Benjamin Schlein (auth.) is a nonfiction available to read on EtoBox.

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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 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

Who reads Effective Evolution Equations from Quantum Dynamics (SpringerBriefs in Mathematical Physics, 7)?

Author

Niels Benedikter, Marcello Porta, Benjamin Schlein (auth.)

Publisher

Springer International Publishing

Published

2016

Language

EN

ISBN

9783319248981

Category

nonfiction

Subjects

Science, Physics, Stem