Design of a high sensitivity and wide range angular rate sensor based on exceptional surface

It is found that when the parity–time symmetry phenomenon is introduced into the resonant optical gyro system and it works near the exceptional point,the sensitivity can in theory be significantly amplified at low angular rate.However,in fact,the exceptional point is easily disturbed by external environmental variables,which means that it depends on harsh experimental environment and strong control ability,so it is difficult to move towards practical application.Here,we propose a new angular rate sensor structure based on exceptional surface,which has the advantages of high sensitivity and high robustness.The system consists of two fiber-optic ring resonators and two optical loop mirrors,and one of the resonators contains a variable ratio coupler and a variable optical attenuator.We theoretically analyze the system response,and the effects of phase and coupling ratio on the system response.Finally,compared with the conventional resonant gyro,the sensitivity of this exceptional surface angular rate sensor can be improved by about 300 times at low speed.In addition,by changing the loss coefficient in the ring resonator,we can achieve a wide range of 600 rad/s.This scheme provides a new approach for the development of ultra-high sensitivity and wide range angular rate sensors in the future.

Exceptional points and quantum dynamics in a non-Hermitian two-qubit system

We study the exceptional-point(EP) structure and the associated quantum dynamics in a system consisting of a non-Hermitian qubit and a Hermitian qubit. We find that the system possesses two sets of EPs, which divide the systemparameter space into PT-symmetry unbroken, partially broken and fully broken regimes, each with distinct quantumdynamics characteristics. Particularly, in the partially broken regime, while the PT-symmetry is generally broken in the whole four-dimensional Hilbert space, it is preserved in a two-dimensional subspace such that the quantum dynamics in the subspace are similar to those in the PT-symmetry unbroken regime. In addition, we reveal that the competition between the inter-qubit coupling and the intra-qubit driving gives rise to a complex pattern in the EP variation with system parameters.

Localization Dynamics at the Exceptional Point of Non-Hermitian Creutz Ladder

We propose a quasi-one-dimensional non-Hermitian Creutz ladder with an entirely flat spectrum by introducing alternating gain and loss components while maintaining inversion symmetry.Destructive interference generates a flat spectrum at the exceptional point,where the Creutz ladder maintains coalesced and degenerate eigenvalues with compact localized states distributed in a single plaquette.All excitations are completely confined within the localization area,unaffected by gain and loss.Single-site excitations exhibit nonunitary dynamics with intensities increasing due to level coalescence,while multiple-site excitations may display oscillating or constant intensities at the exceptional point.These results provide insights into the fascinating dynamics of non-Hermitian localization,where level coalescence and degeneracy coexist at the exceptional point.

EXAMPLES ON EXCEPTIONAL VALUES OF MEROMORPHIC FUNCTIONS

In this paper, by means of the definition of Borel exceptional value method, another exceptional value of meromorphic function which is a T exceptional value is defined by linking the concept of T direction. And we construct a meromorphic function with zero as Borel exceptional value, but not as T exceptional value; and another meromorphic function with zero as T exceptional value, but not as Borel exceptional value.

Reconfigurable metamaterial for asymmetric and symmetric elastic wave absorption based on exceptional point in resonant bandgap

Elastic wave absorption at subwavelength scale is of significance in many engineering applications.Non-Hermitian metamaterials show the ability in high-efficiency wave absorption.However,the single functionality of metamaterials is an important limitation on their practical applications for lack of tunability and reconfigurability.Here,we propose a tunable and reconfigurable non-Hermitian piezoelectric metamaterial bar,in which piezoelectric bars connect with resonant circuits,to achieve asymmetric unidirectional perfect absorption(UPA)and symmetric bidirectional perfect absorption(PA)at low frequencies.The two functions can be arbitrarily switched by rearranging shunted circuits.Based on the reverberation-ray matrix(RRM)method,an approach is provided to achieve UPA by setting an exceptional point(EP)in the coupled resonant bandgap.By using the transfer matrix method(TMM)and the finite element method(FEM),it is observed that a non-Hermitian pseudo-band forms between two resonant bandgaps,and the EP appears at the bottom of the pseudo-band.In addition,the genetic algorithm is used to accurately and efficiently design the shunted circuits for desired low-frequency UPA and PA.The present work may provide new strategies for vibration suppression and guided waves manipulation in wide potential applications.

Exceptional family of elements and the solvability of complementarity problems in uniformly smooth and uniformly convex Banach spaces

The notion of “exceptional family of elements (EFE)” plays a very important role in solving complementarity prob- lems. It has been applied in finite dimensional spaces and Hilbert spaces by many authors. In this paper, by using the generalized projection defined by Alber, we extend this notion from Hilbert spaces to uniformly smooth and uniformly convex Banach spaces, and apply this extension to the study of nonlinear complementarity problems in Banach spaces.

Entanglement of E8E8 Exceptional Lie Symmetry Group Dark Energy, Einstein’s Maximal Total Energy and the Hartle-Hawking No Boundary Proposal as the Explanation for Dark Energy

The present note is concerned with two connected and highly important fundamental questions of physics and cosmology, namely if E8E8 Lie symmetry group describes the universe and where cosmic dark energy comes from. Furthermore, we reason following Wheeler, Hartle and Hawking that since the boundary of a boundary is an empty set which models the quantum wave of the cosmos, then it follows that dark energy is a fundamental physical phenomenon associated with the boundary of the holographic boundary. This leads directly to a clopen universe which is its own Penrose tiling-like multiverse with energy density in full agreement with COBE, WMAP and Type 1a supernova cosmic measurements.

Observation of the exceptional point in superconducting qubit with dissipation controlled by parametric modulation

Open physical systems described by the non-Hermitian Hamiltonian with parity-time-reversal(PT)symmetry show peculiar phenomena,such as the presence of an exceptional point(EP)at which the PT symmetry is broken and two resonant modes of the Hamiltonian become degenerate.Near the EP,the system could be more sensitive to external perturbations and this may lead to enhanced sensing.In this paper,we present experimental results on the observation of PT symmetry broken transition and the EP using a tunable superconducting qubit.The quantum system of investigation is formed by the two levels of the qubit and the energy loss of the system to the environment is controlled by a method of parametric modulation of the qubit frequency.This method is simple with no requirements for additional elements or qubit device modifications.We believe it can be easily implemented on multi-qubit devices that would be suitable for further exploration of non-Hermitian physics in more complex and diverse systems.

Nonlinear perturbation of a high-order exceptional point:Skin discrete breathers and the hierarchical power-law scaling

We study the nonlinear perturbation of a high-order exceptional point(EP)of the order equal to the system site number L in a Hatano-Nelson model with unidirectional hopping and Kerr nonlinearity.Notably,we find a class of discrete breathers that aggregate to one boundary,here named as skin discrete breathers(SDBs).The nonlinear spectrum of these SDBs shows a hierarchical power-law scaling near the EP.Specifically,the response of nonlinear energy to the perturbation is given by E_(m)∝Γ~(α_(m)),whereα_(m)=3^(m-1)is the power with m=1,...,L labeling the nonlinear energy bands.This is in sharp contrast to the L-th root of a linear perturbation in general.These SDBs decay in a double-exponential manner,unlike the edge states or skin modes in linear systems,which decay exponentially.Furthermore,these SDBs can survive over the full range of nonlinearity strength and are continuously connected to the self-trapped states in the limit of large nonlinearity.They are also stable,as confirmed by a defined nonlinear fidelity of an adiabatic evolution from the stability analysis.As nonreciprocal nonlinear models may be experimentally realized in various platforms,such as the classical platform of optical waveguides,where Kerr nonlinearity is naturally present,and the quantum platform of optical lattices with Bose-Einstein condensates,our analytical results may inspire further exploration of the interplay between nonlinearity and non-Hermiticity,particularly on high-order EPs,and benchmark the relevant simulations.

THE ENERGY FUNCTION WITH RESPECT TO THE ZEROS OF THE EXCEPTIONAL HERMITE POLYNOMIALS

We examine the energy function with respect to the zeros of exceptional Hermite polynomials. The localization of the eigenvalues of the Hessian is given in the general case.In some special arrangements we have a more precise result on the behavior of the energy function. Finally we investigate the energy function with respect to the regular zeros of the exceptional Hermite polynomials.

Quantum exceptional points of non-Hermitian Hamiltonian and Liouvillian in dissipative quantum Rabi model

The open quantum system can be described by either a Lindblad master equation or a non-Hermitian Hamiltonian(NHH).However,these two descriptions usually have different exceptional points(EPs),associated with the degeneracies in the open quantum system.Here,considering a dissipative quantum Rabi model,we study the spectral features of EPs in these two descriptions and explore their connections.We find that,although the EPs in these two descriptions are usually different,the EPs of NHH will be consistent with the EPs of master equation in the weak coupling regime.Further,we find that the quantum Fisher information(QFI),which measures the statistical distance between quantum states,can be used as a signature for the appearance of EPs.Our study may give a theoretical guidance for exploring the properties of EPs in open quantum systems.

Fabry–Prot resonance coupling associated exceptional points in a composite grating structure

The exceptional point（EP） is a significant and attractive phenomenon in an open quantum system. The scattering properties of light are similar to those in the open quantum system, which makes it possible to achieve EP in the optic system. Here we investigate the EP in a Fabry–P′erot（F–P） resonant coupling structure. The coupling between different types of F–P resonances leads to a near zero reflection, which results in a degeneration of eigenstates and thus the appearing of EP. Furthermore, the multi-wavelength EPs and unidirectional invisibility can be achieved which may be used in integrated photonics systems.

A Quick Algorithm for Mining Exceptional Rules

Exceptional rules are often ignored because of their small support. However, they have high confidence, so they are useful sometimes. A new algorithm for mining exceptional rules is presented, which creates a large itemset from a relatively small database and scans the whole database only one time to generate all exceptional rules. This algorithm is proved to be quick and effective through its application in a mushroom database.

On Hochschild Homology of Endomorphism Algebras of Exceptional Sequences

In this note, we studied the Hochschild Homology of endomorphism algebras of exceptional sequences over any hereditary algebras.

Exceptionally Preserved Punctatus triangulicostalis and Its Post-embryonic Development

Objective The putative coronatean Punctatus flourished at the beginning of the Cambrian explosion, and is significant in the exploration of the origin and evolution of early life. Liu Yunhuan established a new species： Punctatus triangulicostalis Liu, 2006. Two questions remain： how was the special body plan of P. triangulicostalis formed？ How does P. triangulicostalis transform from embryo to the long cylindrical mature individual？ Although the study of Steiner et al. in 2004 involved the above questions, they did not explain them clearly due to the lack of fossil materials at that time. This article aims to consider the above questions based on new information from several rare specimens.

The Effect of Life Skills Training on the Mental Health and Level of Resilience among Teachers of Normal Students and Teachers of Exceptional Students in Zahedan

This is an experimental study conducted on two groups of control and experimental using pretestposttest design, applying psychological intervention on the study sample. The present study aimed to determine the effectiveness of collective education life skills on mental health and resilience of teachers in Zahedan. The population of the study included all teachers at schools with normal students and teachers at schools with exceptional students in Zahedan, among which 60 teachers at normal schools and 20 teachers at exceptional schools were selected and placed in two groups of experimental and control, respectively. Initially, members of the experimental group were taught 10 basic life skills in 10 2-hour sessions. Mental health and resilience questionnaires were distributed and gathered before and after the training sessions. Results indicated the positive effect of life skills training on mental health of teachers at schools with normal students and teachers at schools with exceptional students, which meant that the more the life skills training to teachers at schools with normal students and teachers at schools with exceptional students, the lower their mental health scores would be. Results also indicated the positive effect of life skills training on resilience of teachers at schools with normal students and teachers at schools with exceptional students, which meant that the more the life skills training to teachers at schools with normal students and teachers at schools with exceptional students, the higher their resilience scores would be.

Are there markers for exceptional responders available for attending pathologists?

In the records of the recent rampant clinical trials,people have noticed there is a fraction,though small,who have ex tremely good responses to the drugs.The definition of this population"Cancer exceptional responder"is proposed and feasibility study has been launched[1].Definition there is not par ticularly hard ones.Classical example is one of 14 bladder cancer patients who participated in Everolimus phase 2 trial,had complete response,and subsequent analysis of DNA of those patients revealed that they had inactivation mutations in TSC1 and NF2,both of which were mTOR regulators[2].

Exceptional Functions of Random Series

We study the random Taylor series whose random variable sequence in |z|＜1 belongs to a class of non equal distributions which are general enough, and proved that they have not almost surely exceptioinal fu nction.

Effective interventions to improve domain-specific social, emotional, or academic outcomes for twice-exceptional individuals who are gifted with ADHD as a disability

The demand for effective interventions to improve domain-specific academic outcomes for individuals with special needs at either end of the spectrum has existed for some time.Since the earlier contributions to the literature documenting gifted individuals who were simultaneously exhibiting disabilities,there has been some progress in our understanding.We now know that in individuals with both gifts and disabilities,potentially,either or both of the exceptionalities can obscure the effects of the other,which significantly delays the average time to receive a diagnosis.Such delays in diagnosis detrimentally impact the the form of effective interventions without a diagnosis.The purpose of this paper is t quality of life across various domains because there can be no opportunity to receive help in o determine whether effective interventions exist to improve domain-specific(i.e.,social,emotional,or academic)outcomes for people with both gifts and disabilities.A query was performed using evidence databases TRIP and PDQ for“twice-exceptional,”“Giftedness,”“Disability,”and“intervention.”The four most relevant,freely available studies in English were selected for critique.Despite identifying potential threats to validity among the studies,methodological similarities among them were strong enough to confidently conclude that not only do effective interventions exist for the population of gifted with ADHD,but the outcomes of these interventions may also carry over into other domains resulting in indirect effects.