2019
Том 71
№ 11

All Issues

Samuliak R. V.

Articles: 2
Brief Communications (Ukrainian)

Generalized Dicke model as an integrable dynamical system inverse to the nonlinear Schrödinger equation

Samuliak R. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 1. - pp. 126–128

We prove that a dynamical system obtained by the space-time inversion of the nonlinear Schrödinger equation is equivalent to a generalized Dicke model. We study the complete Liouville integrability of the obtained dynamical system.

Article (English)

Hamiltonian analysis of exact integrability of the quantum 3-level superradiance Dicke model

Samuliak R. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1256–1264

It is proved that the quantum 3- level superradiance Dicke model is exactly integrable. The Lax representation of the operator system of evolution equations is derived on the basis of a theory of Lie algebras of currents. The method employed in discussions of the quantum inverse scattering problem is applied to obtain quantum analogs of the action-angle variables. The spectra of the energy operator and of other quantum motion integrals as well as the exact one- and multiparticle excitation eigenstates of the model are constructed. It is shown that the model possesses states of constrained quasiparticles (quantum solitons) that induce superradiance pulses.