Open AccessHyperchaos and its control in two-level quantum oscillators lattice
Author(s) -
А. В. Андреев
Publication year - 2019
Publication title -
cybernetics and physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.267
H-Index - 8
eISSN - 2226-4116
pISSN - 2223-7038
DOI - 10.35470/2226-4116-2019-8-3-93-97
Subject(s) - lyapunov exponent , parametric statistics , quantum , mathematics , lattice (music) , physics , quantum system , lyapunov function , statistical physics , control theory (sociology) , quantum mechanics , nonlinear system , control (management) , statistics , computer science , artificial intelligence , acoustics
The behavior of the square lattices of coupled two-level quantum oscillators is investigated. As quantum oscillators, we use the model of Rydberg atoms obtained using the approximation of a fully factorized density matrix. To investigate the behavior of the system the Lyapunov exponents spectra are calculated. Chaos and hyperchaos in the systems are revealed. It was shown that the number of positive Lyapunov exponents almost linearly depends on the number of atoms in the system, at a rate suggesting that adding three atoms leads to the appearance of an additional positive Lyapunov exponent. Using an external parametric effect and continuous feedback is suggested to control the complicated dynamics in the system. Using continuous feedback allows reducing the number of positive Lyapunov exponents from 3 to only 2 while introducing external parametric influence into the system allows reducing their number down to 0and completely suppresses hyperchaos.