52 citations · 64 across the 7 of their papers we have counts for
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Dual Algebraic Pairs and Polynomial Lie Algebras in Quantum Physics: Foundations and Geometric Aspects
V. P. Karassiov
We discuss some aspects and examples of applications of dual algebraic pairs in quantum many-body physics. They arise in models whose Hamiltonians hav…
An implementation of the polynomial Lie algebra methods for solving a class of nonlinear models in quantum optics
V. P. Karassiov, A. A. Gusev, S. I. Vinitsky
We develop some calculation schemes to determine dynamics of a wide class of integrable quantum-optical models using their symmetry adapted reformulation in terms of polynomial Lie…
A Nonlinear Dynamics and New Quasiclassical Solutions for a Class of Quantum Coupled Systems
Valery P. Karassiov
Hamiltonians of a wide-spread class of strongly coupled quantum system models are expressed as nonlinear functions of generators. It enables us to use the formalism…
Polynomial Lie Algebras and Associated Pseudogroup Structures in Composite Quantum Models
Valery P. Karassiov
Polynomial Lie (super)algebras are introduced via -invariant polynomial Jordan maps in quantum composite models with Hamiltonians having invariance groups $G_{i…
variational schemes for solving one class of quantum nonlinear models
V. P. Karassiov
Hamiltonians of a wide-spread class of -invariant nonlinear quantum models, including multiboson and frequency conversion ones, are expressed as non-linear functions of $s…
Polynomial Lie Algebras in Action: Smooth Mappings and Approximations
V. P. Karassiov
We examine applications of polynomial Lie algebras to solve physical tasks in -invariant models of coupled subsystems in quantum physics. A general operator f…