RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
Main page
About this project
Software
Classifications
Links
Terms of Use

Search papers
Search references

RSS
Current issues
Archive issues
What is RSS






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Internat. J. Modern Phys. B, 2013, Volume 27, Issue 8, Pages 1350002–22 (Mi jsphb2)  

The Marsden–Weinstein reduction structure of integrable dynamical systems and a generalized exactly solvable quantum superradiance model

N. N. Bogolyubov (Jr.)a, Ya. A. Prikarpatskyb

a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
b Department of Applied Mathematics, University of Agriculture, Krakow, Poland

Abstract: An approach to describing nonlinear Lax type integrable dynamical systems of modern mathematical and theoretical physics, based on the Marsden–Weinstein reduction method on canonically symplectic manifolds with group symmetry, is proposed. Its natural relationship with the well-known Adler–Kostant–Souriau–Berezin–Kirillov method and the associated R-matrix approach is analyzed.
A new generalized exactly solvable spatially one-dimensional quantum superradiance model, describing a charged fermionic medium interacting with external electromagnetic field, is suggested. The Lax type operator spectral problem is presented, the related R-structure is calculated. The Hamilton operator renormalization procedure subject to a physically stable vacuum is described, the quantum excitations and quantum solitons, related with the thermodynamical equilibrity of the model, are discussed.

DOI: https://doi.org/10.1142/S0217979213500021


Bibliographic databases:

Received: 25.10.2012
Revised: 27.10.2012
Accepted:01.11.2012
Language:

Linking options:
  • http://mi.mathnet.ru/eng/jsphb2

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:14

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020