Volume 125, Number 2, January 2019
|Number of page(s)||7|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||21 February 2019|
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
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.
PACS: 42.65.Yj – Optical parametric oscillators and amplifiers / 84.30.Ng – Oscillators, pulse generators, and function generators / 42.79.Gn – Optical waveguides and couplers
© EPLA, 2019
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