Realizing exceptional points of any order in the presence of symmetry
- URL: http://arxiv.org/abs/2202.07009v1
- Date: Mon, 14 Feb 2022 19:55:34 GMT
- Title: Realizing exceptional points of any order in the presence of symmetry
- Authors: Sharareh Sayyad and Flore K. Kunst
- Abstract summary: Exceptional points(EPs) appear as degeneracies in the spectrum of non-Hermitian matrices.
In general, an EP of order $n$ may find room to emerge if $2(n-1)$ real constraints are imposed.
For two-, three- and four-band systems, we explicitly present the constraints needed for the occurrence of EPs in terms of system parameters.
- Score: 0.0
- License: http://creativecommons.org/publicdomain/zero/1.0/
- Abstract: Exceptional points~(EPs) appear as degeneracies in the spectrum of
non-Hermitian matrices at which the eigenvectors coalesce. In general, an EP of
order $n$ may find room to emerge if $2(n-1)$ real constraints are imposed. Our
results show that these constraints can be expressed in terms of the
determinant and traces of the non-Hermitian matrix. Our findings further reveal
that the total number of constraints may reduce in the presence of unitary and
antiunitary symmetries. Additionally, we draw generic conclusions for the
low-energy dispersion of the EPs. Based on our calculations, we show that in
odd dimensions the presence of sublattice or pseudo-chiral symmetry enforces
$n$th order EPs to disperse with the $(n-1)$th root. For two-, three- and
four-band systems, we explicitly present the constraints needed for the
occurrence of EPs in terms of system parameters and classify EPs based on their
low-energy dispersion relations.
Related papers
- Topological Order in the Spectral Riemann Surfaces of Non-Hermitian Systems [44.99833362998488]
We show topologically ordered states in the complex-valued spectra of non-Hermitian systems.
These arise when the distinctive exceptional points in the energy surfaces of such models are annihilated.
We illustrate the characteristics of the topologically protected states in a non-Hermitian two-band model.
arXiv Detail & Related papers (2024-10-24T10:16:47Z) - Exploiting Exogenous Structure for Sample-Efficient Reinforcement Learning [44.17068570786194]
We study a class of structured Markov Decision Processes (MDPs) known as Exo-MDPs.
Exo-MDPs provide a natural model for various applications, including inventory control, portfolio management, power systems, and ride-sharing.
arXiv Detail & Related papers (2024-09-22T18:45:38Z) - Sample-Efficient Constrained Reinforcement Learning with General Parameterization [35.22742439337603]
We consider a constrained Markov Decision Problem (CMDP) where the goal of an agent is to maximize the expected discounted sum of rewards over an infinite horizon.
We develop the Primal-Dual Accelerated Natural Policy Gradient (PD-ANPG) algorithm that ensures an $epsilon$ global optimality gap and $epsilon$ constraint violation.
arXiv Detail & Related papers (2024-05-17T08:39:05Z) - Symmetry-induced higher-order exceptional points in two dimensions [0.0]
We provide a complete characterization of the appearance of symmetry-induced higher-order EPs in 2D parameter space.
We find that besides EP2s only EP3s, EP4s, and EP5s can be stabilized in 2D.
These higher-order EPs must always appear in pairs with their dispersion determined by the symmetries.
arXiv Detail & Related papers (2024-01-11T18:51:29Z) - Intrinsic Bayesian Cramér-Rao Bound with an Application to Covariance Matrix Estimation [49.67011673289242]
This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a smooth manifold.
It induces a geometry for the parameter manifold, as well as an intrinsic notion of the estimation error measure.
arXiv Detail & Related papers (2023-11-08T15:17:13Z) - Effects of detuning on $\mathcal{PT}$-symmetric, tridiagonal,
tight-binding models [0.0]
Non-Hermitian, tight-binding $mathcalPT$-symmetric models are extensively studied in the literature.
Here, we investigate two forms of non-Hermitian Hamiltonians to study the $mathcalPT$-symmetry breaking thresholds and features of corresponding surfaces of exceptional points (EPs)
Taken together, our results provide a detailed understanding of detuned tight-binding models with a pair of gain-loss potentials.
arXiv Detail & Related papers (2023-02-26T01:36:59Z) - Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized
rotational symmetry [85.36456486475119]
A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system.
Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
arXiv Detail & Related papers (2021-11-24T15:50:22Z) - Symmetry and Higher-Order Exceptional Points [0.0]
We show how physically relevant symmetries make higher-order EPs dramatically more abundant and conceptually richer.
Remarkably, these different symmetries yield topologically distinct types of EPs.
arXiv Detail & Related papers (2021-03-29T16:16:57Z) - $\PT$ Symmetry and Renormalisation in Quantum Field Theory [62.997667081978825]
Quantum systems governed by non-Hermitian Hamiltonians with $PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution.
We show how $PT$ symmetry may allow interpretations that evade ghosts and instabilities present in an interpretation of the theory within a Hermitian framework.
arXiv Detail & Related papers (2021-03-27T09:46:36Z) - $\mathcal{PT}$-symmetry breaking in a Kitaev chain with one pair of
gain-loss potentials [0.0]
Parity-time symmetric systems are governed by non-Hermitian Hamiltonians with exceptional-point (EP) degeneracies.
Here, we obtain the $mathcalPT$-threshold for a one-dimensional, finite Kitaev chain.
In particular, for an even chain with zero on-site potential, we find a re-entrant $mathcalPT$-symmetric phase bounded by second-order EP contours.
arXiv Detail & Related papers (2021-03-12T03:10:45Z) - Perturbation theory near degenerate exceptional points [0.0]
The Hamiltonians $H=H_0+lambda V$ are non-Hermitian and lie close to their unobservable exceptional-point (EP) degeneracy limit.
The method of construction of the bound states is described.
The emergence of a counterintuitive connection between the value of $L$, the structure of the matrix elements of perturbations, and the possible loss of the stability and unitarity of the processes of the unfolding of the EP is given a detailed explanation.
arXiv Detail & Related papers (2020-08-02T13:28:00Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.