The Marsden-Weinstein reduction structure of integrable dynamical systems and a generalized exactly solvable quantum superradiance model
N. N. Bogolubov jr. , Yarema A. Prykarpatskyy
AbstractAn 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.
|Journal series||International Journal of Modern Physics B, ISSN 0217-9792, (A 15 pkt)|
|Publication size in sheets||1.05|
|Keywords in English||Marsden-Weinstein reduction, integrability, R-matrix, dynamical systems|
|License||Journal (articles only); author's original; ; after publication|
|Publication indicators||: 2014 = 0.421; : 2013 = 0.455 (2) - 2013=0.359 (5)|
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