$sl(2)$ variational schemes for solving one class of quantum nonlinear models$sl(2)$ variational schemes for solving one class of quantum nonlinear models

V. P. Karassiov

Hamiltonians of a wide-spread class of $G_{inv}$ -invariant nonlinear quantum models, including multiboson and frequency conversion ones, are expressed as non-linear functions of $sl(2)$ generators. It enables us to use standard variational schemes, based on $sl(2)$ generalized coherent states as trial functions, for solving both spectral and evolution tasks. In such a manner a new analytical expression is found for energy spectra in a mean-field approximation which is beyond quasi-equidistant ones obtained earlier.Hamiltonians of a wide-spread class of $G_{inv}$-invariant nonlinear quantum models, including multiboson and frequency conversion ones, are expressed as non-linear functions of $sl(2)$ generators. It enables us to use standard variational schemes, based on $sl(2)$ generalized coherent states as trial functions, for solving both spectral and evolution tasks. In such a manner a new analytical expression is found for energy spectra in a mean-field approximation which is beyond quasi-equidistant ones obtained earlier.

arXiv:quant-ph/9608016Aug 12, 19960 citations

Variational Methods for Quantum Systems

Philipp O. J. Scherer

Graduate texts in physicsJan 1, 20171 citation

QUANTUM-MECHANICAL SYSTEMS AS DYNAMICAL SYSTEMS ON SL(2, R)

Jonáš Kulhánek

Il Nuovo Cimento BOct 1, 19980 citations

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

V. P. Karassiov

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.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.

arXiv:quant-ph/9710012Oct 2, 19971 citation

VARIATIONAL METHODS IN QUANTUM MECHANICS

Béla Gazdy

Periodica Polytechnica Mechanical EngineeringJan 1, 19776 citations

Asymptotic expressions of path curve for a class of Fermi gases in nonlinear disturbed mechanism

Shi Lan-Fang, Xianfeng Chen, Han Xiang-Lin +2 more

The model of nonlinear disturbed mechanism for one-dimensional Fermi gas is investigated. Firstly, the corresponding functional is constructed; secondly, its Lagrange operator is selected; using the modified generalized variational iteration method, the approximate analytic solutions of corresponding path curves are obtained. A simple example is given, and the approximation accuracy obtained by using the modified generalized variational iteration method is shown to be better. The aim of this article is to provide a valid method of solving the nonlinear physical problems.The model of nonlinear disturbed mechanism for one-dimensional Fermi gas is investigated. Firstly, the corresponding functional is constructed; secondly, its Lagrange operator is selected; using the modified generalized variational iteration method, the approximate analytic solutions of corresponding path curves are obtained. A simple example is given, and the approximation accuracy obtained by using the modified generalized variational iteration method is shown to be better. The aim of this article is to provide a valid method of solving the nonlinear physical problems.

Acta Physica SinicaJan 1, 20140 citations

sl(2)

variational schemes for solving one class of quantum nonlinear models

Hamiltonians of a wide-spread class of

G_{inv}

-invariant nonlinear quantum models, including multiboson and frequency conversion ones, are expressed as non-linear functions of

sl(2)

generators. It enables us to use standard variational schemes, based on

sl(2)

generalized coherent states as trial functions, for solving both spectral and evolution tasks. In such a manner a new analytical expression is found for energy spectra in a mean-field approximation which is beyond quasi-equidistant ones obtained earlier.

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.