A fractal square F is essentially a planar self-similar set satisfying the set equation F=(F+D)/n with n≥2 and D?{0,1,...,n-1}~2.In this paper,we study the topological classification of fractal squares in the case of...A fractal square F is essentially a planar self-similar set satisfying the set equation F=(F+D)/n with n≥2 and D?{0,1,...,n-1}~2.In this paper,we study the topological classification of fractal squares in the case of n=4 and |D|=4.展开更多
In this paper the problem of topological classification of ordinary 3D)and planar(2D)spin states in a ferromagnet including an annular cavity is discussed. It is verified that the set of homotopy classes of either 3D ...In this paper the problem of topological classification of ordinary 3D)and planar(2D)spin states in a ferromagnet including an annular cavity is discussed. It is verified that the set of homotopy classes of either 3D or 2D spin states in such ordered medium can be constructed into the groups isomorphic to Z, the additive group of integers.展开更多
Topological band theory has been studied for free fermions for decades,and one of the most profound physical results is the bulk-boundary correspondence.Recently a focus in topological physics is extending topological...Topological band theory has been studied for free fermions for decades,and one of the most profound physical results is the bulk-boundary correspondence.Recently a focus in topological physics is extending topological classification to mixed states.Here,we focus on Gaussian mixed states for which the modular Hamiltonians of the density matrix are quadratic free fermion models with U(1)symmetry and can be classified by topological invariants.The bulk-boundary correspondence is then manifested as stable gapless modes of the modular Hamiltonian and degenerate spectrum of the density matrix.In this article,we show that these gapless modes can be detected by the full counting statistics,mathematically described by a function introduced as F(θ).A divergent derivative atθ=πcan be used to probe the gapless modes in the modular Hamiltonian.Based on this,a topological indicator,whose quantization to unity senses topologically nontrivial mixed states,is introduced.We present the physical intuition of these results and also demonstrate these results with concrete models in both one-and two-dimensions.Our results pave the way for revealing the physical significance of topology in mixed states.展开更多
this paper,we base our analysis on the assumption that the existence of a photon sphere is an intrinsic characteristic of any ultra-compact gravitational structure with spherical symmetry.Utilizing the concept of a to...this paper,we base our analysis on the assumption that the existence of a photon sphere is an intrinsic characteristic of any ultra-compact gravitational structure with spherical symmetry.Utilizing the concept of a topological photon sphere,we categorize the behaviors of various gravitational models based on the structure of their photon spheres.This innovative approach enables us to define boundaries for black hole parameters,subsequently enabling us to classify the model as either a black hole or naked singularity.We demonstrate that the presence of this interplay between the gravitational structure and the existence of a photon sphere is a unique advantage that can be utilized from both perspectives.Our observations indicate that a gravitational model typically exhibits the behavior ofa horizonless structure(or naked singularity)when a minimum effective potential(a stable photon sphere)appears within the studied spacetime region.Additionally,in this study,we investigate the effect of this structure on the behavior of the photon sphere by selecting models that are affected by Perfect Fluid Dark Matter(PFDM).Finally,by analyzing a model with multiple event horizons,we show that the proposed method remains applicable evenin suchscenarios.展开更多
Non-Hermitian(NH)systems have revealed unique topological phenomena that are not observed in Hermitian counterparts,such as novel topology classifications and the NH skin effect.In periodic NH systems,eigenenergies be...Non-Hermitian(NH)systems have revealed unique topological phenomena that are not observed in Hermitian counterparts,such as novel topology classifications and the NH skin effect.In periodic NH systems,eigenenergies become complex and exhibit windings in the complex plane,while eigenstate winding numbers,which are strictly integers in Hermitian systems,can take half-integer values.However,direct experimental observation of NH winding of both eigenenergies and eigenstates,especially the half-integer winding,remains a significant challenge.In this work,we utilize the orbital angular momentum(OAM)synthetic dimension to construct an NH topological lattice and achieve direct observation of both eigenstate and eigenenergy windings.We report the first experimental observation of a half-integer eigenstate winding number,and reveal the intrinsic relationship between the direction in the NH skin dynamics and eigenenergy windings.Furthermore,by partitioning the OAM chain into two semi-infinite chains,we observe zero boundary modes and demonstrate that their distributions are jointly determined by the winding numbers of both the eigenstates and eigenenergies.This work provides comprehensive insights into NH topologies and offers a new experimental platform for exploring NH phenomena.展开更多
In this paper,we investigate the topological charge and conditions for the existence of the photon sphere in Kiselev-anti-de Sitter(AdS)black holes within f(R,T)gravity.Furthermore,we establish their topological class...In this paper,we investigate the topological charge and conditions for the existence of the photon sphere in Kiselev-anti-de Sitter(AdS)black holes within f(R,T)gravity.Furthermore,we establish their topological classifications.We employ two different methods based on Duan's topological current p-mapping theory viz analysis of temperature and the generalized Helmholtz free energy methods to study the topological classes of our black hole.Considering this black hole,we discuss the critical and zero points(topological charges and topological numbers)for different parameters.Our findings reveal that the Kiselev parameter o and f(R,T)gravity parameter y influence the number of topological charges of black holes,providing novel insights into topological classifications.We observe that for given values of the free parameters,total topological charges(Q_(total)=-1)exist for the T method and total topological numbers(ω=+1)for the generalized Helmholtz free energy method.Our research findings elucidate that,in contrast to the scenario in whichω=1/3,in other cases,increasing y increases the number of total topological charges for the black hole.Interestingly,for the phantom field(ω=-4/3),we observe that decreasingγincreases the number of topological charges.Additionally,we study the results for the photon sphere.The studied models reveal that the simultaneous presence ofγandωeffectively expands the permissible range forγ.In other words,the model can exhibit black hole behavior over a larger domain.Additionally,we observe that with the stepwise reduction ofγ,the region covered by singularity diminishes and becomes more restricted.However,an interesting point about all three ranges is the elimination of the forbidden region in this model.In other words,this model and the investigated areas appear to have no region in which both theφand metric functions simultaneously lack solutions.Additionally,we fully check the curvatures singularities and energy conditions for the mentioned black hole.展开更多
Equilibrium points and periodic orbits in irregular gravitational fields are significant for an understanding of dynamical behaviors around asteroids as well as deep space exploring missions. The dipole segment is a g...Equilibrium points and periodic orbits in irregular gravitational fields are significant for an understanding of dynamical behaviors around asteroids as well as deep space exploring missions. The dipole segment is a good alternative model to study qualitative dynamical properties near dumbbell-shaped asteroids. In this paper, the dipole segment model and its equilibrium points are simply introduced. The stability of the two triangular equilibrium points of the system is numerically examined. Next, periodic orbits are presented around the dipole segment model in two different cases, in which triangular equilibria are linearly stable and unstable,respectively. New types of periodic orbits are illustrated in detail, including their orbital shapes, periods and the Jacobi integral.The orbital stability, topological classification and bifurcations of these orbits are also analyzed with numerical continuations.展开更多
基金Supported by the Soft Science Research of Xiangyang City in 2019。
文摘A fractal square F is essentially a planar self-similar set satisfying the set equation F=(F+D)/n with n≥2 and D?{0,1,...,n-1}~2.In this paper,we study the topological classification of fractal squares in the case of n=4 and |D|=4.
文摘In this paper the problem of topological classification of ordinary 3D)and planar(2D)spin states in a ferromagnet including an annular cavity is discussed. It is verified that the set of homotopy classes of either 3D or 2D spin states in such ordered medium can be constructed into the groups isomorphic to Z, the additive group of integers.
基金supported by the National Key R&D Program of China(Grant No.2023YFA1406702)the Innovation Program for Quantum Science and Technology 2021ZD0302005+1 种基金the XPLORER Prizepartly supported by the Start-up Research Fund of Southeast University(RF1028624190)。
文摘Topological band theory has been studied for free fermions for decades,and one of the most profound physical results is the bulk-boundary correspondence.Recently a focus in topological physics is extending topological classification to mixed states.Here,we focus on Gaussian mixed states for which the modular Hamiltonians of the density matrix are quadratic free fermion models with U(1)symmetry and can be classified by topological invariants.The bulk-boundary correspondence is then manifested as stable gapless modes of the modular Hamiltonian and degenerate spectrum of the density matrix.In this article,we show that these gapless modes can be detected by the full counting statistics,mathematically described by a function introduced as F(θ).A divergent derivative atθ=πcan be used to probe the gapless modes in the modular Hamiltonian.Based on this,a topological indicator,whose quantization to unity senses topologically nontrivial mixed states,is introduced.We present the physical intuition of these results and also demonstrate these results with concrete models in both one-and two-dimensions.Our results pave the way for revealing the physical significance of topology in mixed states.
文摘this paper,we base our analysis on the assumption that the existence of a photon sphere is an intrinsic characteristic of any ultra-compact gravitational structure with spherical symmetry.Utilizing the concept of a topological photon sphere,we categorize the behaviors of various gravitational models based on the structure of their photon spheres.This innovative approach enables us to define boundaries for black hole parameters,subsequently enabling us to classify the model as either a black hole or naked singularity.We demonstrate that the presence of this interplay between the gravitational structure and the existence of a photon sphere is a unique advantage that can be utilized from both perspectives.Our observations indicate that a gravitational model typically exhibits the behavior ofa horizonless structure(or naked singularity)when a minimum effective potential(a stable photon sphere)appears within the studied spacetime region.Additionally,in this study,we investigate the effect of this structure on the behavior of the photon sphere by selecting models that are affected by Perfect Fluid Dark Matter(PFDM).Finally,by analyzing a model with multiple event horizons,we show that the proposed method remains applicable evenin suchscenarios.
基金supported by the Innovation Program for Quantum Science and Technology(Grant Nos.2021ZD0301400 and 2021ZD0301200)the National Natural Science Foundation of China(Grants No.11874343,92365205,11974334,12404576,and W2411001)+3 种基金the Postdoctoral Innovative Talents Support program(BX20230349)China Postdoctoral Science Foundation Funded Project(2024M763125)Xiaomi Young Talents Program,the Fundamental Research Funds for the Central Universities(Grant No.WK2030000085)the USTC Major Frontier Research Program(Grant No.LS2030000002).
文摘Non-Hermitian(NH)systems have revealed unique topological phenomena that are not observed in Hermitian counterparts,such as novel topology classifications and the NH skin effect.In periodic NH systems,eigenenergies become complex and exhibit windings in the complex plane,while eigenstate winding numbers,which are strictly integers in Hermitian systems,can take half-integer values.However,direct experimental observation of NH winding of both eigenenergies and eigenstates,especially the half-integer winding,remains a significant challenge.In this work,we utilize the orbital angular momentum(OAM)synthetic dimension to construct an NH topological lattice and achieve direct observation of both eigenstate and eigenenergy windings.We report the first experimental observation of a half-integer eigenstate winding number,and reveal the intrinsic relationship between the direction in the NH skin dynamics and eigenenergy windings.Furthermore,by partitioning the OAM chain into two semi-infinite chains,we observe zero boundary modes and demonstrate that their distributions are jointly determined by the winding numbers of both the eigenstates and eigenenergies.This work provides comprehensive insights into NH topologies and offers a new experimental platform for exploring NH phenomena.
文摘In this paper,we investigate the topological charge and conditions for the existence of the photon sphere in Kiselev-anti-de Sitter(AdS)black holes within f(R,T)gravity.Furthermore,we establish their topological classifications.We employ two different methods based on Duan's topological current p-mapping theory viz analysis of temperature and the generalized Helmholtz free energy methods to study the topological classes of our black hole.Considering this black hole,we discuss the critical and zero points(topological charges and topological numbers)for different parameters.Our findings reveal that the Kiselev parameter o and f(R,T)gravity parameter y influence the number of topological charges of black holes,providing novel insights into topological classifications.We observe that for given values of the free parameters,total topological charges(Q_(total)=-1)exist for the T method and total topological numbers(ω=+1)for the generalized Helmholtz free energy method.Our research findings elucidate that,in contrast to the scenario in whichω=1/3,in other cases,increasing y increases the number of total topological charges for the black hole.Interestingly,for the phantom field(ω=-4/3),we observe that decreasingγincreases the number of topological charges.Additionally,we study the results for the photon sphere.The studied models reveal that the simultaneous presence ofγandωeffectively expands the permissible range forγ.In other words,the model can exhibit black hole behavior over a larger domain.Additionally,we observe that with the stepwise reduction ofγ,the region covered by singularity diminishes and becomes more restricted.However,an interesting point about all three ranges is the elimination of the forbidden region in this model.In other words,this model and the investigated areas appear to have no region in which both theφand metric functions simultaneously lack solutions.Additionally,we fully check the curvatures singularities and energy conditions for the mentioned black hole.
基金supported by the National Natural Science Foundation of China(Grant Nos.11602019&11572035)the Young Elite Scientist Sponsorship Program by China Association for Science and Technology(Grant No.2016QNRC001)Excellent Young Teachers Program of Beijing Institute of Technology(Grant No.2015YG0605)
文摘Equilibrium points and periodic orbits in irregular gravitational fields are significant for an understanding of dynamical behaviors around asteroids as well as deep space exploring missions. The dipole segment is a good alternative model to study qualitative dynamical properties near dumbbell-shaped asteroids. In this paper, the dipole segment model and its equilibrium points are simply introduced. The stability of the two triangular equilibrium points of the system is numerically examined. Next, periodic orbits are presented around the dipole segment model in two different cases, in which triangular equilibria are linearly stable and unstable,respectively. New types of periodic orbits are illustrated in detail, including their orbital shapes, periods and the Jacobi integral.The orbital stability, topological classification and bifurcations of these orbits are also analyzed with numerical continuations.
