Energy transport and Anderson-like localization in non-Hermitian electrical transmission line

Abstract

We investigate on the right and left-handed (RH/LH) balanced gain and loss non-Hermitian electrical transmission lines (ETL) modeled using an imaginary resistor. The hamiltonian of each system is successfully derived in the framework of the tight-binding theory. We discuss the underlying symmetries and calculate the breaking thresholds of the Parity time (PT) and Anti PT (APT) symmetry phase transitions. Moreover, the modes dynamic characterization reveal the existence of critical points beyond which operation requires thresholdless transition and the eigen modes are either real or complex. We also present a self-consistent theory to investigate on their scattering properties. In particular, we demonstrate that the Anderson-like localized modes mostly emerge in the broken phase where eigen modes are complex with the localization length proportional to the cell numbers. Importantly, the mode localization is most likely to occur in structures consisting of a large cells number for RH ETL while LH ETL will confined modes even for infinitesimal small cell numbers. These results unveil embryonic applications in cryptography, switching and system control.

Hall conductance of a non-Hermitian Weyl semimetal

“…This system's structural characterization and dispersive properties reveal a broad range of strong coupling, where the interplay between control and probe fields induces unique transport properties. Additionally, investigations into structures like NH trimers and electronic dimer systems with an imaginary resistor shed light on unique dispersive properties and multiple windows of transparency, further enriching our understanding of scattering and transport phenomena in NH waveguides and electrical setups [85][86][87]. Thus, given the recent experimental advances, we believe that our findings on the Hall conductance can be realized in state-of-the-art platforms.…”

Non-reciprocal transmission of coupled LC resonators through parity-time symmetry breaking

“…For those operating at the EPs, the enhanced sensitivity of sensors constructed by LC resonators has been implemented [7][8][9]. Moreover, PT-symmetric direct electrical transmission lines show a phase transition from real to complex eigenvalues, and the emerging Anderson-like localized modes in the broken phase can be utilized in applications for controlling the flow of energy such as switching [10,11]. In particular, for those operating at the broken PT-symmetric regime, the complex-conjugate frequencies behave with the same real eigenfrequencies but the opposite signs of the imaginary parts, leading to oscillations magnitudes with an exponentially growing mode and an exponentially decaying mode.…”

PT-symmetric electronic dimer without gain material

“…Among non-Hermitian Hamiltonians, it belongs to those that are invariant under the joint transformations of spatial reflection (parity ) and temporal inversion (time-reversal  ) which may admit real eigenvalues. This particular class of Hamiltonians, called  -symmetric Hamiltonians, was first introduced in Quantum Mechanics in 1998 by Carl Bender and Stephan Boettcher [1], before rapidly spreading to other branches of physics as optics [2][3][4][5], photonics [4,6], mechanics [7][8][9][10] and electronics [11][12][13][14][15], to mention a few.  -symmetric Hamiltonians generally require that gain and loss into the system should be balanced, so that, as the degree of non-Hermiticity (also called gain/loss parameter) is increased, the system exhibits a transition from  exact phase with real frequencies to  broken phase, where the frequencies become complex.…”