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

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.