A model of three coupled wave guides and third order exceptional points

Heiss, W. D.; Wunner, Günter

doi:10.1088/1751-8113/49/49/495303

Cited by 39 publications

(38 citation statements)

References 29 publications

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“…The dimension of the Jordan block is given by N , the number of coalescing levels. Following the convention in the literature, we refer to an EP involving the coalescence of N levels as an EPN [56][57][58]; however, in the case of two coalescing levels (EP2) considered in this paper we find it useful to introduce two further subcategories, following the convention introduced in Ref. [52].…”

Section: Introductionmentioning

confidence: 99%

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

Garmon

Ordóñez

2017

Journal of Mathematical Physics

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It has been reported in the literature that the survival probability P (t) near an exceptional point where two eigenstates coalesce should generally exhibit an evolution P (t) ∼ t 2 e −Γt , in which Γ is the decay rate of the coalesced eigenstate; this has been verified in a microwave billiard experiment [B. Dietz, et al., Phys. Rev. E 75, 027201 (2007)]. However, the heuristic effective Hamiltonian that is usually employed to obtain this result ignores the possible influence of the continuum threshold on the dynamics. By contrast, in this work we employ an analytical approach starting from the microscopic Hamiltonian representing two simple models in order to show that the continuum threshold has a strong influence on the dynamics near exceptional points in a variety of circumstances. To report our results, we divide the exceptional points in Hermitian open quantum systems into two cases: at an EP2A two virtual bound states coalesce before forming a resonance, anti-resonance pair with complex conjugate eigenvalues, while at an EP2B two resonances coalesce before forming two different resonances. For the EP2B, which is the case studied in the microwave billiard experiment, we verify the survival probability exhibits the previously reported modified exponential decay on intermediate timescales, but this is replaced with an inverse power law on very long timescales. Meanwhile, for the EP2A the influence from the continuum threshold is so strong that the evolution is non-exponential on all timescales and the heuristic approach fails completely. When the EP2A appears very near the threshold we obtain the novel evolution P (t) ∼ 1 − C1 √ t on intermediate timescales, while further away the parabolic decay (Zeno dynamics) on short timescales is enhanced.

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Section: Introductionmentioning

confidence: 99%

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

Garmon

Ordóñez

2017

Journal of Mathematical Physics

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“…In much rarer cases exceptional points of higher order (EPN ) are discussed [27][28][29][30]. In a matrix representation they can be identified by the fact that the matrix is not diagonalisable.…”

Section: Introductionmentioning

confidence: 99%

Simple Models of Three Coupled Pt -Symmetric Wave Guides Allowing for Third-Order Exceptional Points

Schnabel¹,

Cartarius²,

Main³

et al. 2017

Acta Polytech

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Abstract.We study theoretical models of three coupled wave guides with a PT -symmetric distribution of gain and loss. A realistic matrix model is developed in terms of a three-mode expansion. By comparing with a previously postulated matrix model it is shown how parameter ranges with good prospects of finding a third-order exceptional point (EP3) in an experimentally feasible arrangement of semiconductors can be determined. In addition it is demonstrated that continuous distributions of exceptional points, which render the discovery of the EP3 difficult, are not only a feature of extended wave guides but appear also in an idealised model of infinitely thin guides shaped by delta functions.

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“…Also the progress in the underlying theory of the localization of EPNs is not too quick. Its characteristic nontrivial N = 3 implementation as proposed in [34] consisted, for example, of a mere triplet of coupled wave-guides, with the gain and loss areas arranged in a PT −symmetric manner. An experimentally feasible arrangement of the semiconductor wave-guides has been determined.…”

Section: Exceptional Points: Theory Vs Experimentsmentioning

confidence: 99%

Generalized Bose–Hubbard Hamiltonians exhibiting a complete non-Hermitian degeneracy

Znojil

2019

Annals of Physics

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The method of construction of the tridiagonal and symmetric complex-matrix Hamiltonians H (N ) (z) exhibiting an exceptional-point (EP) degeneracy of the Nth (i.e., maximal) order at a preselected parameter z = z (EP N ) = 1 is proposed and tested. In general, the implementation of the method requires the use of computer-assisted symbolic manipulations, especially at the larger matrix dimensions N. The well known PT −symmetric N-by-N-matrix Bose-Hubbard Hamiltonians as well as their recent N ≤ 5 non-Bose-Hubbard alternatives as obtained as special solutions. Several other N ≥ 6 non-Bose-Hubbard models H (N ) (z) exhibiting the maximal EPN degeneracy are also constructed and analyzed in detail. In particular, their z−dependent, real or complex spectra of energies are displayed and discussed near as well as far from z (EP N ) .

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A model of three coupled wave guides and third order exceptional points

Cited by 39 publications

References 29 publications

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

Simple Models of Three Coupled Pt -Symmetric Wave Guides Allowing for Third-Order Exceptional Points

Generalized Bose–Hubbard Hamiltonians exhibiting a complete non-Hermitian degeneracy

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