Designing non-Hermitian real spectra through electrostatics

Yang, Russell; Tan, Jun Wei; Tai, Tommy; Koh, Jin; Li, Linhu; Longhi, Stefano; Lee, Ching Hua

doi:10.1016/j.scib.2022.08.005

Cited by 26 publications

(7 citation statements)

References 70 publications

(89 reference statements)

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“…In the context of electrostatic theory, the electric potential distribution inside an area of interest in the vicinity of a grounded conducting plate can be obtained by placing an image charge reflected across the conducting plate [90][91][92][93][94][101][102][103]. The image charge causes equipotential (which is considered zero for a grounded conductor) throughout the surface of the plate and thus satisfies the boundary conditions of the grounded conducting plate.…”

Section: Methods Of Images For Analytic Impedance Formulae Across Bou...mentioning

confidence: 99%

“…Two issues that present challenges in forming full analogies with condensed matter are the finite circuit boundaries (which differ from the usual open boundary conditions) and the homogeneity of the lattice array -while computations can certainly be performed numerically, a comprehensive analytical expression for the impedance in heterogeneous finite circuits has yet to be obtained. One way to implement boundary conditions in electrostatic theory is through the method of images, in which the boundaries are replaced by image charges located opposite the original charges [90][91][92][93][94]. As a demonstration of this approach, we apply the method of images to periodic tilings of finite electric circuit networks to compute the two-point impedance of the finite circuit networks.…”

Section: Introductionmentioning

confidence: 99%

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Impedance responses and size-dependent resonances in topolectrical circuits via the method of images

Sahin

Siu

Rafi-Ul-Islam

et al. 2022

Preprint

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Resonances in an electric circuit occur when capacitive and inductive components are present together. Such resonances appear in admittance measurements depending on the circuit’s parameters and the driving AC frequency. In this study, we analyze the impedance characteristics of nontrivial topolectrical circuits (TEs) such as 1D and 2D Su–Schrieffer–Heeger (SSH) circuits and reveal that size-dependent anomalous impedance resonances inevitably arise in finite LC circuits. Through the method of images, we study how resonance modes in a multi-dimensional circuit array can be nontrivially modified by the reflection and interference of current from the structure and boundaries of the lattice. We derive analytic expressions for the impedance across two corner nodes of various lattice networks with homogeneous and heterogeneous circuit elements. We also derive the irregular dependency of the impedance resonance on the lattice size, and provide integral and dimensionally-reduced expressions for the impedance in three dimensions and above.

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Section: Methods Of Images For Analytic Impedance Formulae Across Bou...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Impedance responses and size-dependent resonances in topolectrical circuits via the method of images

Sahin

Siu

Rafi-Ul-Islam

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…This very general result follows from the fact that the spectral amplitudes ψ 1,2 (k) exp(iEk/F ), with ψ 1,2 (k) solutions to the Sturm-Liouville problem [Eqs. (43,44)], are periodic and continuously differentiable functions of k and thus their Fourier coefficients ān , bn decay as n → ±∞ at least like ∼ 1/n, regardless of the value of λ.…”

Section: B Wannier-stark Laddersmentioning

confidence: 99%

“…in models where the dynamics is described by an effective non-Hermitian Hamiltonian [31][32][33] which accounts for energy/particle * stefano.longhi@polimi.it exchange with external reservoirs. A remarkable property of certain classes of non-Hermitian Hamiltonians is to display an entirely real energy spectrum in spite of non-Hermiticity [34][35][36][37][38][39][40][41][42][43][44]. Among such Hamiltonians, great attention has been devoted to the ones displaying parity-time (PT ) symmetry [34][35][36], a concept that has become very popular in the past decade and found important applications in photonics and beyond [45][46][47][48][49][50][51].…”

Section: Introductionmentioning

confidence: 99%

Complex Berry phase and imperfect non-Hermitian phase transitions

Longhi¹,

Li²

2023

Preprint

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In many classical and quantum systems described by an effective non-Hermitian Hamiltonian, spectral phase transitions, from an entirely real energy spectrum to a complex spectrum, can be observed as a non-Hermitian parameter in the system is increased above a critical value. A paradigmatic example is provided by systems possessing parity-time (PT ) symmetry, where the energy spectrum remains entirely real in the unbroken PT phase while a transition to complex energies is observed in the unbroken PT phase. Such spectral phase transitions are universally sharp. However, when the system is slowly and periodically cycled, the phase transition can become smooth, i.e. imperfect, owing to the complex Berry phase associated to the cyclic adiabatic evolution of the system. This remarkable phenomenon is illustrated by considering the spectral phase transition of the Wannier-Stark ladders in a PT -symmetric class of two-band non-Hermitian lattices subjected to an external dc field, unraveling that a non-vanishing imaginary part of the Zak phase -the Berry phase picked up by a Bloch eigenstate evolving across the entire Brillouin zone-is responsible for imperfect spectral phase transitions.

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“…There exist several physical incarnations that can be used to explore the non-Hermitian systems [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] , including the cold atoms [48][49][50][51] , electrical circuits [52][53][54][55][56][57] , photonic and acoustic systems [58][59][60][61][62] . Among them, electric circuits have been widely used because the circuit structure can be flexibly designed to facilitate integration and mass production.…”

Section: Experimental Implementationmentioning

confidence: 99%

Anomalous non-Hermitian skin effect: the topological inequivalence of skin modes versus point gap

Guo¹,

Bao²,

Zhu³

et al. 2023

Preprint

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Non-Hermitian skin effect, the localization of an extensive number of open boundary eigenstates at the boundaries of the system, has greatly expanded the frontier of physical laws. It has long been believed that the present of skin modes is equivalent to the topologically nontrivial point gap. However, we find that this concomitance can be broken, i.e., the skin modes can be present or absent whereas the point gap is topologically trivial or nontrivial, respectively, named anomalous non-Hermitian skin effect. This anomalous phenomenon arises whenever the unidirectional hopping amplitudes among subsystems are emergence, in which sub-chains have the decoupling-like behaviors and only contribute to the energy levels while without particle occupation. The occurrence of the anomalous non-Hermitian skin effect is accompanied by the mutations of the open boundary eigenvalues, whose structure exhibits the multifold exceptional point and can not be recovered by continuum bands. Moreover, an experimental setup using circuits is proposed to simulate this novel effect. Our results reveal the topologically inequivalent between skin modes and point gap. This new effect not only can give a deeper understanding of non-Bloch theory and the critical phenomenon in non-Hermitian systems, but may also inspire new applications such as in the sensors field.

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Designing non-Hermitian real spectra through electrostatics

Cited by 26 publications

References 70 publications

Impedance responses and size-dependent resonances in topolectrical circuits via the method of images

Impedance responses and size-dependent resonances in topolectrical circuits via the method of images

Complex Berry phase and imperfect non-Hermitian phase transitions

Anomalous non-Hermitian skin effect: the topological inequivalence of skin modes versus point gap

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