The strong connection between braids and knots provides valuable insights into studying the topological state and phase classification of various physical systems.The phenomenon of non-Hermitian(NH)two-and three-band ...The strong connection between braids and knots provides valuable insights into studying the topological state and phase classification of various physical systems.The phenomenon of non-Hermitian(NH)two-and three-band braiding has received widespread attention.However,a systematic exploration and visualization of non-Abelian braiding and the associated knot transformations in four-band systems remains unexplored.Here,we propose a theoretical model of NH four-band braiding,provide its phase diagram,and establish its trivial,Abelian,and non-Abelian braiding rules.Additionally,we report on special knots,such as the Hopf and Solomon links in braided knots,and reveal that their transformations are accompanied by and mediated through exceptional points.Our work provides a detailed case for studying NH multiband braiding and knot structures in four-band systems,which could offer insights for topological photonics and analog information processing applications.展开更多
Temporal logics are often adopted as basic tools to specifying mental states such as belief and goal of agents. Although there are works on non-monotonic extension of linear temporal logic (LTL) and branching time tem...Temporal logics are often adopted as basic tools to specifying mental states such as belief and goal of agents. Although there are works on non-monotonic extension of linear temporal logic (LTL) and branching time temporal logic (CTL),the non-monotonic extension of alternating-time temporal logic (ATL) which is an important kind of multi-agent cooperation logics has not been discussed yet in literature. To solve this problem,this paper proposed non-monotonic alternating-time temporal logic with belief and goal,namely N-ATL-BG,to facilitate the non-monotonic reasoning of mental states of agents. The semantic model,syntax and semantics of this new logic are developed. A model checking algorithm which can be finished in polynomial time is proposed for this new logic. Examples are given to show its usage.展开更多
Topological phases featuring non-Abelian charges have garnered significant attention in recent years.In parallel,the study of multiband exceptional topology in non-Hermitian systems has emerged as a prominent research...Topological phases featuring non-Abelian charges have garnered significant attention in recent years.In parallel,the study of multiband exceptional topology in non-Hermitian systems has emerged as a prominent research direction.In this study,we investigate a parity-time(PT)symmetric Hamiltonian,which hosts both conventional non-Abelian topological phases(NATPs)and hybrid phases.We propose an experimental scheme using spin-1 atoms with spin-orbit coupling trapped in two-dimensional(2D)lattices.Before adding a non-Hermitian term,we find the emergence of distinct topological phases mixed by two NATPs and establish their connection with NATPs theory.When a non-Hermitian term that preserves PT symmetry protection was introduced,stable second-order exceptional rings and third-order exceptional points emerge and they drive the edge states to manifest as discontinuous Fermi arcs in the surface Brillouin zone.However,with the variation of the non-Hermitian term,it is rather intriguing that two types of exceptional rings here transition from being internally tangent to externally tangent,transforming into a new topological phase equivalent to the Hermitian case.This research provides deeper insights into the nature of NATPs and the topological implications of exceptional structures,contributing to the field of topological physics.展开更多
We explore the parity-time(PT)-symmetry breaking transition in a dimer circuit composed of two RLC resonators that are weakly coupled via an inductor.The energy behavior of this dimer circuit is reflected in the split...We explore the parity-time(PT)-symmetry breaking transition in a dimer circuit composed of two RLC resonators that are weakly coupled via an inductor.The energy behavior of this dimer circuit is reflected in the splitting or degeneracy of the systems eigenfrequencies as the gain–loss strength varies.Its dynamical properties can be described by a non-Hermitian Hamiltonian.The eigenfrequency spectrum of the system is divided by two critical points into three distinct regions:the symmetric region,the oscillatory growth region,and the fully exponential growth region.Building upon previous work on implementing the exceptional point(EP)in circuit systems,our study focuses on further exploring the variation patterns of circuit eigenfrequencies near the EP under weak coupling conditions.In addition,we construct a corresponding Dirac point(DP)circuit system for comparison.By leveraging the unique physical properties near both the EP and the DP,we further propose potential practical applications.Using perturbation theory and system simulations,we demonstrate that the square-root eigenfrequency splitting near the EP significantly enhances the sensitivity to small external perturbations,compared to the linear splitting behavior near the DP.This study presents promising prospects for next-generation sensing technologies.展开更多
In this paper, we investigate the effect of exceptional points(EPs) on the violation of Leggett–Garg inequality(LGI) and no-signaling-in-time(NSIT) conditions and compare the different effects between the Hamiltonian...In this paper, we investigate the effect of exceptional points(EPs) on the violation of Leggett–Garg inequality(LGI) and no-signaling-in-time(NSIT) conditions and compare the different effects between the Hamiltonian EP(HEP) and Liouvillian EP(LEP) on those violations. We consider an open system consisting of two coupled qubits and each qubit is contacted with a thermal bath at a different temperature. In the case of omitting quantum jumps, we find that the system exhibits a second-order HEP, which separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI and NSIT conditions can be violated in both regimes and not violated at the HEP. In the case of without omitting quantum jumps, we find that the system exhibits a third-order LEP, which also separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI can only be violated in the underdamped regime with large coupling strength between the qubits.Conversely, the NSIT conditions can be violated in both regimes, as well as at the LEP, except in the overdamped regime with small coupling strength between the qubits. Comparing the violations of the LGI and NSIT conditions with HEP and LEP, we find that the quantum jumps would reduce the generation of coherence, enhance the decoherence, and lead to narrower parameter regimes that the LGI and NSIT conditions can be violated. Furthermore, in both cases,the NSIT conditions can be violated in a wider parameter regime than the LGI.展开更多
Developing chemically complex intermetallic alloys(CCIMAs)is considered an effective strategy for overcoming the serious brittleness of conventional intermetallic alloys,especially under a high stress level.However,mo...Developing chemically complex intermetallic alloys(CCIMAs)is considered an effective strategy for overcoming the serious brittleness of conventional intermetallic alloys,especially under a high stress level.However,most CCIMAs still struggle to achieve yield strengths exceeding gigapascals,limiting their use as reliable structural materials in many engineering fields.展开更多
The unique wave-manipulation capabilities of zero-index metamaterials(ZIMs)offer a new opportunity for realizing bound states in the continuum(BICs).However,the relationship between anomalous scattering and BICs remai...The unique wave-manipulation capabilities of zero-index metamaterials(ZIMs)offer a new opportunity for realizing bound states in the continuum(BICs).However,the relationship between anomalous scattering and BICs remains underexplored when parity–time(PT)symmetry is introduced.In this work,we demonstrate that a BIC splits into a pair of lasing modes carrying opposite topological charges by introducing PT symmetry through gain-loss cylinders embedded in ZIM layers.Theoretical analysis and numerical simulations reveal that lasing and unidirectional transparency phenomena result from the singularities and exceptional points of the scattering matrix.Moreover,exceptional points can be tuned via propagation phase modulation in the air gap,and their coalescence produces quasi-BICs with symmetric responses.This work provides a framework for manipulating BICs and topological lasing modes in non-Hermitian systems,offering new insights for designing non-Hermitian photonic devices.展开更多
To solve the problems that the exception handling code is hard to test and maintain and that it affects the robustness and reliability of software, a method for evaluating the exception handling of programs is present...To solve the problems that the exception handling code is hard to test and maintain and that it affects the robustness and reliability of software, a method for evaluating the exception handling of programs is presented. The exception propagation graph （EPG） that describes the large programs with exception handling constructs is proposed by simplifying the control flow graph and it is applied to a case to verify its validity. According to the EPG, the exception handling code that never executes is identified; the points that are the most critical to controlling exception propagation are found; and the irrational exception handling code is corrected. The constructing algorithm for the EPG is given; thus, this provides a basis for automatically constructing the EPG and automatically correcting the irrational exception handling code.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.62575099,62075059,61405058)Guangdong Basic and Applied Basic Research Foundation(Grant No.2024A1515011353)+2 种基金Open Project of the State Key Laboratory of Advanced Optical Communication Systems and Networks of China(Grant No.2024GZKF20)the Natural Science Foundation of Hunan Province(Grant Nos.2020JJ4161 and 2017JJ2048)Scientific Research Foundation of Hunan Provincial Education Department(Grant No.21A0013)。
文摘The strong connection between braids and knots provides valuable insights into studying the topological state and phase classification of various physical systems.The phenomenon of non-Hermitian(NH)two-and three-band braiding has received widespread attention.However,a systematic exploration and visualization of non-Abelian braiding and the associated knot transformations in four-band systems remains unexplored.Here,we propose a theoretical model of NH four-band braiding,provide its phase diagram,and establish its trivial,Abelian,and non-Abelian braiding rules.Additionally,we report on special knots,such as the Hopf and Solomon links in braided knots,and reveal that their transformations are accompanied by and mediated through exceptional points.Our work provides a detailed case for studying NH multiband braiding and knot structures in four-band systems,which could offer insights for topological photonics and analog information processing applications.
基金Natural Science Foundation of Fujian Province of China ( No.2006J0316)College Scientific and Technological Project of Office of Education of Fujian Province of China ( No.JB09302)Scientific Research Foundation for Young Teachers ofFujian Agriculture and Forestry University, China (No.08B21)
文摘Temporal logics are often adopted as basic tools to specifying mental states such as belief and goal of agents. Although there are works on non-monotonic extension of linear temporal logic (LTL) and branching time temporal logic (CTL),the non-monotonic extension of alternating-time temporal logic (ATL) which is an important kind of multi-agent cooperation logics has not been discussed yet in literature. To solve this problem,this paper proposed non-monotonic alternating-time temporal logic with belief and goal,namely N-ATL-BG,to facilitate the non-monotonic reasoning of mental states of agents. The semantic model,syntax and semantics of this new logic are developed. A model checking algorithm which can be finished in polynomial time is proposed for this new logic. Examples are given to show its usage.
基金supported by the National Natural Science Foundation of China(Grant Nos.12274473 and 12135018).
文摘Topological phases featuring non-Abelian charges have garnered significant attention in recent years.In parallel,the study of multiband exceptional topology in non-Hermitian systems has emerged as a prominent research direction.In this study,we investigate a parity-time(PT)symmetric Hamiltonian,which hosts both conventional non-Abelian topological phases(NATPs)and hybrid phases.We propose an experimental scheme using spin-1 atoms with spin-orbit coupling trapped in two-dimensional(2D)lattices.Before adding a non-Hermitian term,we find the emergence of distinct topological phases mixed by two NATPs and establish their connection with NATPs theory.When a non-Hermitian term that preserves PT symmetry protection was introduced,stable second-order exceptional rings and third-order exceptional points emerge and they drive the edge states to manifest as discontinuous Fermi arcs in the surface Brillouin zone.However,with the variation of the non-Hermitian term,it is rather intriguing that two types of exceptional rings here transition from being internally tangent to externally tangent,transforming into a new topological phase equivalent to the Hermitian case.This research provides deeper insights into the nature of NATPs and the topological implications of exceptional structures,contributing to the field of topological physics.
基金the financial support of the Natural Science Foundation of Jiangsu Province(Grant No.BK20231320)。
文摘We explore the parity-time(PT)-symmetry breaking transition in a dimer circuit composed of two RLC resonators that are weakly coupled via an inductor.The energy behavior of this dimer circuit is reflected in the splitting or degeneracy of the systems eigenfrequencies as the gain–loss strength varies.Its dynamical properties can be described by a non-Hermitian Hamiltonian.The eigenfrequency spectrum of the system is divided by two critical points into three distinct regions:the symmetric region,the oscillatory growth region,and the fully exponential growth region.Building upon previous work on implementing the exceptional point(EP)in circuit systems,our study focuses on further exploring the variation patterns of circuit eigenfrequencies near the EP under weak coupling conditions.In addition,we construct a corresponding Dirac point(DP)circuit system for comparison.By leveraging the unique physical properties near both the EP and the DP,we further propose potential practical applications.Using perturbation theory and system simulations,we demonstrate that the square-root eigenfrequency splitting near the EP significantly enhances the sensitivity to small external perturbations,compared to the linear splitting behavior near the DP.This study presents promising prospects for next-generation sensing technologies.
基金financially supported by the National Natural Science Foundation of China (Grants Nos. 11775019 and 11875086)。
文摘In this paper, we investigate the effect of exceptional points(EPs) on the violation of Leggett–Garg inequality(LGI) and no-signaling-in-time(NSIT) conditions and compare the different effects between the Hamiltonian EP(HEP) and Liouvillian EP(LEP) on those violations. We consider an open system consisting of two coupled qubits and each qubit is contacted with a thermal bath at a different temperature. In the case of omitting quantum jumps, we find that the system exhibits a second-order HEP, which separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI and NSIT conditions can be violated in both regimes and not violated at the HEP. In the case of without omitting quantum jumps, we find that the system exhibits a third-order LEP, which also separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI can only be violated in the underdamped regime with large coupling strength between the qubits.Conversely, the NSIT conditions can be violated in both regimes, as well as at the LEP, except in the overdamped regime with small coupling strength between the qubits. Comparing the violations of the LGI and NSIT conditions with HEP and LEP, we find that the quantum jumps would reduce the generation of coherence, enhance the decoherence, and lead to narrower parameter regimes that the LGI and NSIT conditions can be violated. Furthermore, in both cases,the NSIT conditions can be violated in a wider parameter regime than the LGI.
基金financially supported by the National Natural Science Foundation of China(Nos.52222112,52101151 and 52101135)Hong Kong Research Grant Council(RGC)(No.C1020-21G)+1 种基金Shenzhen Science and Technology Program(No.RCBS20210609103202012)APT research was conducted at the Inter-University 3D APT Unit of City University of Hong Kong(CityU),which is supported by the CityU grant 9360161
文摘Developing chemically complex intermetallic alloys(CCIMAs)is considered an effective strategy for overcoming the serious brittleness of conventional intermetallic alloys,especially under a high stress level.However,most CCIMAs still struggle to achieve yield strengths exceeding gigapascals,limiting their use as reliable structural materials in many engineering fields.
基金supported by the National Natural Science Foundation of China(Grant Nos.12504361,12274313,and 62465005)the Natural Science Foundation of Guangxi(Grant No.2025GXNSFBA069179)the Guangxi Colleges and Universities Young and Middle-aged Teachers’Basic Scientific Research Ability Enhancement Project(Grant No.2025KY0093)。
文摘The unique wave-manipulation capabilities of zero-index metamaterials(ZIMs)offer a new opportunity for realizing bound states in the continuum(BICs).However,the relationship between anomalous scattering and BICs remains underexplored when parity–time(PT)symmetry is introduced.In this work,we demonstrate that a BIC splits into a pair of lasing modes carrying opposite topological charges by introducing PT symmetry through gain-loss cylinders embedded in ZIM layers.Theoretical analysis and numerical simulations reveal that lasing and unidirectional transparency phenomena result from the singularities and exceptional points of the scattering matrix.Moreover,exceptional points can be tuned via propagation phase modulation in the air gap,and their coalescence produces quasi-BICs with symmetric responses.This work provides a framework for manipulating BICs and topological lasing modes in non-Hermitian systems,offering new insights for designing non-Hermitian photonic devices.
基金The National Natural Science Foundation of China(No60503020)the National Basic Research Program of China (973Program) (No2002CB312000)+1 种基金the Natural Science Foundation of Jiangsu Province (NoBK2006094)the Science Research Foundation of China University of Mining and Technology
文摘To solve the problems that the exception handling code is hard to test and maintain and that it affects the robustness and reliability of software, a method for evaluating the exception handling of programs is presented. The exception propagation graph （EPG） that describes the large programs with exception handling constructs is proposed by simplifying the control flow graph and it is applied to a case to verify its validity. According to the EPG, the exception handling code that never executes is identified; the points that are the most critical to controlling exception propagation are found; and the irrational exception handling code is corrected. The constructing algorithm for the EPG is given; thus, this provides a basis for automatically constructing the EPG and automatically correcting the irrational exception handling code.
