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

N. N. Bogolubov jr. , Yarema A. Prykarpatskyy

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.
Author N. N. Bogolubov jr.
N. N. Bogolubov jr.,,
-
, Yarema A. Prykarpatskyy (FoEEaLS / DoAM)
Yarema A. Prykarpatskyy,,
- Department of Applied Mathematics
Journal seriesInternational Journal of Modern Physics B, ISSN 0217-9792, (A 15 pkt)
Issue year2013
Vol27
No8
Pages1-22
Publication size in sheets1.05
Keywords in EnglishMarsden-Weinstein reduction, integrability, R-matrix, dynamical systems
ASJC Classification3104 Condensed Matter Physics; 3109 Statistical and Nonlinear Physics
DOIDOI:10.1142/S0217979213500021
URL http://arxiv.org/pdf/1210.1744.pdf
Internal identifierWIŚIG/2013/211
Languageen angielski
LicenseJournal (articles only); author's original; Other open licence; after publication
Score (nominal)15
Score sourcejournalList
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2014 = 0.421; WoS Impact Factor: 2013 = 0.455 (2) - 2013=0.359 (5)
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OświadczenieYarema Prykarpatskyy
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