It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics.When the domain of...It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics.When the domain of S is restricted to the space of constant scalar curvature metrics,there has been a conjecture that a critical point is also Einstein or isometric to a standard sphere.In the Riemannian case,it’s tangent space satisfies a decomposition.In this paper,we prove that if we only consider the Hermitian metrics,it also have a decomposition.Then we obtain the equation of the critical points among the Hermitian metrics.展开更多
The integration of acoustic vortices with chiral exceptional points (CEPs) in ring cavities enables the controlled unidirectional coupling and manipulation of orbital angular momentum (OAM) modes. However, realizing m...The integration of acoustic vortices with chiral exceptional points (CEPs) in ring cavities enables the controlled unidirectional coupling and manipulation of orbital angular momentum (OAM) modes. However, realizing multiple vortex orders within a single cavity remains challenging because non-Hermitian modulations must be tailored for different OAM modes simultaneously. We propose a simple approach for constructing multiple CEPs by arranging resistive and reactive impedance-boundary modulations with specific azimuthal patterns along the inner wall of an acoustic ring cavity. This design allows for independent engineering of multiple OAM eigenmodes and their simultaneous excitation using a single monopole source. As a representative example, we demonstrate first-, second-, and third-order OAM generation in both an exact PT-symmetric cavity with balanced gain and loss and a loss-biased passive counterpart that offers additional chirality control through the chirality-reversal effect. This study provides a flexible and compact framework for generating and manipulating multi-order acoustic OAM modes on non-Hermitian platforms.展开更多
In this paper,we introduce and prove three analytic results related to uniform convergence,properties of Newtonian potential,and convergence of sequences in Sobolev space constrained by their Laplacian.Then,utilizing ...In this paper,we introduce and prove three analytic results related to uniform convergence,properties of Newtonian potential,and convergence of sequences in Sobolev space constrained by their Laplacian.Then,utilizing our analytic results,we develop a complete proof of a crucial estimate appearing in the results of Guofang Wang and Xiaohua Zhu,which states the classification of extremal Hermitian metrics with finite energy and area on compact Riemann surfaces and finite singularities satisfying small singular angles.展开更多
In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the u...In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.展开更多
We investigate electron mesoscopic transport in a three-terminal setup with coupled quantum dots and a magnetic flux.By mapping the original transport problem into a non-Hermitian Hamiltonian form,we study the interpl...We investigate electron mesoscopic transport in a three-terminal setup with coupled quantum dots and a magnetic flux.By mapping the original transport problem into a non-Hermitian Hamiltonian form,we study the interplay between the coherent couplings between quantum dots,the magnetic flux,and the dissipation due to the tunnel coupling with the reservoirs.展开更多
Quantization noise caused by analog-to-digital converter(ADC)gives rise to the reliability performance degradation of communication systems.In this paper,a quantized non-Hermitian symmetry(NHS)orthogonal frequency-div...Quantization noise caused by analog-to-digital converter(ADC)gives rise to the reliability performance degradation of communication systems.In this paper,a quantized non-Hermitian symmetry(NHS)orthogonal frequency-division multiplexing-based visible light communication(OFDM-VLC)system is presented.In order to analyze the effect of the resolution of ADC on NHS OFDM-VLC,a quantized mathematical model of NHS OFDM-VLC is established.Based on the proposed quantized model,a closed-form bit error rate(BER)expression is derived.The theoretical analysis and simulation results both confirm the effectiveness of the obtained BER formula in high-resolution ADC.In addition,channel coding is helpful in compensating for the BER performance loss due to the utilization of lower resolution ADC.展开更多
The Dicke model,which describes the collective interaction between an ensemble of atoms and a single-mode photon field,serves as a fundamental framework for studying light-matter interactions and quantum electrodynami...The Dicke model,which describes the collective interaction between an ensemble of atoms and a single-mode photon field,serves as a fundamental framework for studying light-matter interactions and quantum electrodynamic phenomena.In this work,we investigate the manifestation of non-Hermitian effects in a generalized Dicke model,where two dissipative atom ensembles interact with a single-mode photon field.We explore the system in the semiclassical limit as a non-Hermitian Dicke model,revealing rich exceptional points(EPs)and diabolic points.Furthermore,we explore the quantum signature of EPs in the Hilbert space,relying on discrete photon numbers.The transition of photons from antibunching to bunching at steady state is unravelled.Our findings deepen the understanding of non-Hermitian physics in light-matter interaction,which is instructive for the design of advanced photonic devices.展开更多
We theoretically explore a non-Hermitian superfluid model with complex-valued interaction, inspired by two-body loss stemming from inelastic scattering observed in ultracold atomic experiments. Utilizing both the righ...We theoretically explore a non-Hermitian superfluid model with complex-valued interaction, inspired by two-body loss stemming from inelastic scattering observed in ultracold atomic experiments. Utilizing both the right-eigenstate-based mean-field theory and its biorthogonal counterpart, we study the properties of the system. Notably, the right-eigenstate-based framework produces smooth and continuous solutions, in stark contrast to the absence of nontrivial solutions and the abrupt discontinuities observed in the biorthogonal-eigenstatebased framework under moderate dissipation. In addition, the lower condensation energy obtained in the former framework suggests its superior suitability for describing this system. Furthermore, we explore the impact of backscattering, a crucial factor in realistic systems. Our analysis reveals that, facilitated by two-body loss, even moderate backscattering destabilizes the superfluid state. Sufficiently strong backscattering completely destroys it, highlighting a key mechanism for the fragility of this non-Hermitian quantum phase.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.12171140).
文摘It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics.When the domain of S is restricted to the space of constant scalar curvature metrics,there has been a conjecture that a critical point is also Einstein or isometric to a standard sphere.In the Riemannian case,it’s tangent space satisfies a decomposition.In this paper,we prove that if we only consider the Hermitian metrics,it also have a decomposition.Then we obtain the equation of the critical points among the Hermitian metrics.
基金supported by the National Natural Science Foundation of China (Grant Nos.92263208,12104383,12304494,and 12404534)the National Key R&D Program of China (Grant No.2022YFA1404400)+1 种基金the Basic and Frontier Exploration Project Independently Deployed by the Institute of Acoustics,Chinese Academy of Sciences (Grant No.JCQY202403)Fundamental Research Funds for the Central Universities。
文摘The integration of acoustic vortices with chiral exceptional points (CEPs) in ring cavities enables the controlled unidirectional coupling and manipulation of orbital angular momentum (OAM) modes. However, realizing multiple vortex orders within a single cavity remains challenging because non-Hermitian modulations must be tailored for different OAM modes simultaneously. We propose a simple approach for constructing multiple CEPs by arranging resistive and reactive impedance-boundary modulations with specific azimuthal patterns along the inner wall of an acoustic ring cavity. This design allows for independent engineering of multiple OAM eigenmodes and their simultaneous excitation using a single monopole source. As a representative example, we demonstrate first-, second-, and third-order OAM generation in both an exact PT-symmetric cavity with balanced gain and loss and a loss-biased passive counterpart that offers additional chirality control through the chirality-reversal effect. This study provides a flexible and compact framework for generating and manipulating multi-order acoustic OAM modes on non-Hermitian platforms.
基金Supported by the National Natural Science Foundation of China(11971450)partially supported by the Project of Stable Support for Youth Team in Basic Research Field,CAS(YSBR-001)。
文摘In this paper,we introduce and prove three analytic results related to uniform convergence,properties of Newtonian potential,and convergence of sequences in Sobolev space constrained by their Laplacian.Then,utilizing our analytic results,we develop a complete proof of a crucial estimate appearing in the results of Guofang Wang and Xiaohua Zhu,which states the classification of extremal Hermitian metrics with finite energy and area on compact Riemann surfaces and finite singularities satisfying small singular angles.
文摘In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1404400)the National Natural Science Foundation of China(Grant No.12125504 and 12305050)+2 种基金Zhejiang Provincial Natural Science Foundation of China(Grant No.LZ25A050001)the Hundred Talents Program of the Chinese Academy of Sciencesthe Natural Science Foundation of Jiangsu Higher Education Institutions of China(Grant No.23KJB140017)。
文摘We investigate electron mesoscopic transport in a three-terminal setup with coupled quantum dots and a magnetic flux.By mapping the original transport problem into a non-Hermitian Hamiltonian form,we study the interplay between the coherent couplings between quantum dots,the magnetic flux,and the dissipation due to the tunnel coupling with the reservoirs.
基金supported by the National Natural Science Foundation of China(No.62201508)the Zhejiang Provincial Natural Science Foundation of China(Nos.LZ21F010001 and LQ23F010004)the State Key Laboratory of Millimeter Waves of Southeast University,China(No.K202212).
文摘Quantization noise caused by analog-to-digital converter(ADC)gives rise to the reliability performance degradation of communication systems.In this paper,a quantized non-Hermitian symmetry(NHS)orthogonal frequency-division multiplexing-based visible light communication(OFDM-VLC)system is presented.In order to analyze the effect of the resolution of ADC on NHS OFDM-VLC,a quantized mathematical model of NHS OFDM-VLC is established.Based on the proposed quantized model,a closed-form bit error rate(BER)expression is derived.The theoretical analysis and simulation results both confirm the effectiveness of the obtained BER formula in high-resolution ADC.In addition,channel coding is helpful in compensating for the BER performance loss due to the utilization of lower resolution ADC.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1404400)the National Natural Science Foundation of China(Grant Nos.12125504 and 12305050)+3 种基金Zhejiang Provincial Natural Science Foundation(Grant No.LZ25A050001)the Doctoral Support Program for Young Talents of the China Association for Science and Technologythe Hundred Talents Program of the Chinese Academy of Sciencesthe Natural Science Foundation of Jiangsu Higher Education Institutions of China(Grant No.23KJB140017)。
文摘The Dicke model,which describes the collective interaction between an ensemble of atoms and a single-mode photon field,serves as a fundamental framework for studying light-matter interactions and quantum electrodynamic phenomena.In this work,we investigate the manifestation of non-Hermitian effects in a generalized Dicke model,where two dissipative atom ensembles interact with a single-mode photon field.We explore the system in the semiclassical limit as a non-Hermitian Dicke model,revealing rich exceptional points(EPs)and diabolic points.Furthermore,we explore the quantum signature of EPs in the Hilbert space,relying on discrete photon numbers.The transition of photons from antibunching to bunching at steady state is unravelled.Our findings deepen the understanding of non-Hermitian physics in light-matter interaction,which is instructive for the design of advanced photonic devices.
基金financially supported by the National Key Research and Development Program of China (Grant No.2024YFA1409001)the National Natural Science Foundation of China (Grants Nos.12374037 and 12204044)+1 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No.XDB28000000)the Fundamental Research Funds for the Central Universities。
文摘We theoretically explore a non-Hermitian superfluid model with complex-valued interaction, inspired by two-body loss stemming from inelastic scattering observed in ultracold atomic experiments. Utilizing both the right-eigenstate-based mean-field theory and its biorthogonal counterpart, we study the properties of the system. Notably, the right-eigenstate-based framework produces smooth and continuous solutions, in stark contrast to the absence of nontrivial solutions and the abrupt discontinuities observed in the biorthogonal-eigenstatebased framework under moderate dissipation. In addition, the lower condensation energy obtained in the former framework suggests its superior suitability for describing this system. Furthermore, we explore the impact of backscattering, a crucial factor in realistic systems. Our analysis reveals that, facilitated by two-body loss, even moderate backscattering destabilizes the superfluid state. Sufficiently strong backscattering completely destroys it, highlighting a key mechanism for the fragility of this non-Hermitian quantum phase.
