Affiliation:
1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
2. 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.
Publisher
World Scientific Pub Co Pte Lt
Subject
Condensed Matter Physics,Statistical and Nonlinear Physics