arXiv subjects

Valery P. Karassiov

Publications and source records attributed to Valery P. Karassiov.

4 recordsLinked to original sources

arXiv1998

Symmetry as a source of hidden coherent structures in quantum physics: general outlook and examples

A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries of their Hamiltonians $H$. Its general ideas are manifested on some recent new examples: 1) G-invariant bi-photons and a related SU(2)-invariant treatment of unpolarized light; 2) quasi-spin clusters in nonlinear models of quantum optics; 3) construction of composite particles and (para)fields from G-invariant clusters due to internal symmetries.

quant-ph↗

arXiv1997

A Nonlinear $sl(2)$ Dynamics and New Quasiclassical Solutions for a Class of Quantum Coupled Systems

Hamiltonians of a wide-spread class of strongly coupled quantum system models are expressed as nonlinear functions of $sl(2)$ generators. It enables us to use the $sl(2)$ formalism, in particular, $sl(2)$ generalized coherent states (GCS) for solving both spectral and evolution tasks. In such a manner, using standard variational schemes with $sl(2)$ GCS as trial functions we find new analytical expressions for energy spectra and non-linear evolution equations for cluster dynamics variables in mean-field approximations which are beyond quasi-harmonic ones obtained earlier. General results are illustrated on certain concrete models of quantum optics and laser physics.

quant-ph↗

arXiv1997

Polynomial Lie Algebras and Associated Pseudogroup Structures in Composite Quantum Models

Polynomial Lie (super)algebras $g_{pd}$ are introduced via $G_{i}$-invariant polynomial Jordan maps in quantum composite models with Hamiltonians $H$ having invariance groups $G_{i}$. Algebras $g_{pd}$ have polynomial structure functions in commutation relations, are related to pseudogroup structures $\exp V, V\in g_{pd}$ and describe dynamic symmetry of models under study. Physical applications of algebras $g_{pd}$ in quantum optics and in composite field theories are briefly discussed.

quant-ph↗

arXiv1994

An Algebraic Approach to Solving Evolution Problems in Some Nonlinear Quantum Models

A new general Lie-algebraic approach is proposed to solving evolution tasks in some nonlinear problems of quantum physics with polynomially deformed Lie algebras $su_{pd}(2)$ as their dynamic symmetry algebras. The method makes use of an expansion of the evolution operators by power series in the $su_{pd}(2)$ shift operators and a (recursive) reduction of finding coefficient functions to solving auxiliary exactly solvable $su(2)$ problems with quadratic Hamiltonians. PACS numbers: 03.70; 02.20; 42.50

hep-th↗