Non-Hermitian Hamiltonian of two-level systems in complex quaternionic space: An introduction in electronics

¹ Laboratory of Mechanics, Materials and Structures, Department of Physics, Faculty of Science, University of Yaounde I - P.O. Box 812,Yaounde, Cameroon
² Nonlinear Physics and Complex Systems Group, Department of Physics, The Higher Teacher's Training College, University of Yaounde I - P.O. Box 47, Yaounde, Cameroon
³ Laboratory of Electronics and Signal Processing, Department of Electrical and Telecommunication Engineering, National Advanced School of Engineering, University of Yaounde I - P.O. Box 8390, Yaounde, Cameroon
⁴ Department of Physics, Faculty of Science, University of Buea - P.O. Box 63, Buea, Cameroon
⁵ Institute of Wood Technologies, University of Yaounde I - P.O. Box 306, Mbalmayo, Cameroon

Received: 7 August 2018
Accepted: 15 January 2019

Abstract

An imaginary resistor (Z) based electronic dimer is used to describe the gyroscopic and resistive coupled two-level systems in quaternionic space. We successfully used the quaternionic coefficients to characterize the different classes of non-Hermitian systems: the pseudo-Hermitian and anti-Hermitian, both having exceptional points (EPs) separating the exact and the broken phases. Remarkably, the EPs conical dynamic is fully described to follow a hyperbolic/parabolic shape in the case of parity-time symmetry (PTS)/anti-PTS, respectively. Interestingly, our results demonstrated that the gyroscopic coupling mechanism allows identical non-dissipative but non-oscillatory systems with negative capacitor to exhibit PTS-like behavior.