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Effective Evolution Equations from Quantum Dynamics by Niels Benedikter - Paperback
949.00 EGP

Effective Evolution Equations from Quantum Dynamics by Niels Benedikter - Paperback

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949.00 EGP 

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Category Type
Physics
ISBN
9783319248967
Author
Various
Publisher
Springer International Publishing AG
Description:

These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrodinger 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 ...

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    Specifications

    Category Type
    Physics
    ISBN
    9783319248967
    EAN-13
    9783319248967
    Item EAN
    2724445779625
    People
    Author
    Various
    Category Type
    Physics
    ISBN
    9783319248967
    EAN-13
    9783319248967
    Item EAN
    2724445779625
    People
    Author
    Various
    People
    Publisher
    Springer International Publishing AG
    Technical Information
    Binding
    Paperback
    Languages and countries
    Book Language
    English
    Read more
  •  

    Description:

    These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrodinger dynamics in certain physically interesting regimes. The focus is primarily on the derivation of time-dependent effective theories

    These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrodinger 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 semi classical 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.

    Product Features:
    • Category Type: Physics
    • Author: Niels Benedikter, Marcello Porta and Benjamin Schlein
    • ISBN: 9783319248967
    • Binding: Paperback
    • Book Language: English
    • Publisher: Springer International Publishing AG
    • Number of Pages: 98
    • Weight: 0.17 kg
    • Book Origin: Switzerland
    • Publication Year: 2015
    • Series: SpringerBriefs in Mathematical Physics
 

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