The authors show that ifΘ=(θ_(jk))is a 3×3 totally irrational real skewsymmetric matrix,whereθ_(jk)∈[0,1)for j,k=1,2,3,then for anyε>0,there existsδ>0 satisfying the following:For any unital C^(*)-alg...The authors show that ifΘ=(θ_(jk))is a 3×3 totally irrational real skewsymmetric matrix,whereθ_(jk)∈[0,1)for j,k=1,2,3,then for anyε>0,there existsδ>0 satisfying the following:For any unital C^(*)-algebra A with the cancellation property,strict comparison and nonempty tracial state space,any four unitaries u1,u2,u3,w∈A such that(1)■,wujw-1=uj-1,w2=1A for j,k=1,2,3;(2)τ(aw)=0 and■for all n∈N,all a∈C^(*)(u1,u2,u3),j,k=1,2,3 and all tracial statesτon A,where C^(*)(u1,u2,u3)is the C^(*)-subalgebra generated by u1,u2 and u3,there exists a 4-tuple of unitaries■in A such that■and■for j,k=1,2,3.The above conclusion is also called that the rotation relations of three unitaries with the flip action is stable under the above conditions.展开更多
The relation between conflict and governance has been dominated by type of government rather than by system of government.With increasing conflict in countries with ethnic and religious diversity,the debate has gradua...The relation between conflict and governance has been dominated by type of government rather than by system of government.With increasing conflict in countries with ethnic and religious diversity,the debate has gradually shifted to understand better the link between conflict and system of government.There is a growing evidence that suggests federal system performs better than unitary system in managing diversity and reducing conflict.Decentralization is even seen to be more effective than federal system not only in managing diversity and reducing conflict but also in delivering public goods.This article provides an account of evolution of system of government in South Sudan.It finds a clear association of centralized unitary system with violent conflict and a relative peace during period of decentralized government or federal system.A decentralized federal system may be appropriate for South Sudan in managing diversity and mitigating conflict.Despite the popular demand by their citizens for a federal system to manage diversity and reduce violent conflict,the ruling elites in the post-independent South Sudan adopted instead an autocratic centralized unitary system that contributed among other factors to the persistent violent conflicts,erosion of social cohesion,and rising mistrust between state and citizens and between and among the communities of South Sudan.展开更多
We give a new result on the construction of K-frame generators for unitary systems by using the pseudo-inverses of involved operators,which provides an improvement to one known result on this topic.We also introduce t...We give a new result on the construction of K-frame generators for unitary systems by using the pseudo-inverses of involved operators,which provides an improvement to one known result on this topic.We also introduce the concept of K-woven generators for unitary systems,by means of which we investigate the weaving properties of K-frame generators for unitary systems.展开更多
On a compact Riemann surface with finite punctures P_(1),…P_(k),we define toric curves as multivalued,totallyunramified holomorphic maps to P^(n)with monodromy in a maximal torus of PSU(n+1).Toric solutions to SU(n+1...On a compact Riemann surface with finite punctures P_(1),…P_(k),we define toric curves as multivalued,totallyunramified holomorphic maps to P^(n)with monodromy in a maximal torus of PSU(n+1).Toric solutions to SU(n+1)Todasystems on X\{P_(1);…;P_(k)}are recognized by the associated toric curves in.We introduce character n-ensembles as-tuples of meromorphic one-forms with simple poles and purely imaginary periods,generating toric curves on minus finitelymany points.On X,we establish a correspondence between character-ensembles and toric solutions to the SU(n+1)system with finitely many cone singularities.Our approach not only broadens seminal solutions with two conesingularities on the Riemann sphere,as classified by Jost-Wang(Int.Math.Res.Not.,2002,(6):277-290)andLin-Wei-Ye(Invent.Math.,2012,190(1):169-207),but also advances beyond the limits of Lin-Yang-Zhong’s existencetheorems(J.Differential Geom.,2020,114(2):337-391)by introducing a new solution class.展开更多
Optical orbital angular momentum(OAM)mode multiplexing has emerged as a promising technique for boosting communication capacity.However,most existing studies have concentrated on channel(de)-multiplexing,overlooking t...Optical orbital angular momentum(OAM)mode multiplexing has emerged as a promising technique for boosting communication capacity.However,most existing studies have concentrated on channel(de)-multiplexing,overlooking the critical aspect of channel routing.This challenge involves the reallocation of multiplexed OAM modes across both spatial and temporal domains—a vital step for developing versatile communication networks.To address this gap,we introduce a novel approach based on the time evolution of OAM modes,utilizing the orthogonal conversion and diffractive modulation capabilities of unitary transformations.This approach facilitates high-dimensional orthogonal transformations of OAM mode vectors,altering both the propagation direction and the spatial location.Using Fresnel diffraction matrices as unitary operators,it manipulates the spatial locations of light beams during transmission,breaking the propagation invariance and enabling temporal evolution.As a demonstration,we have experimentally implemented the deep routing of four OAM modes within two distinct time sequences.Achieving an average diffraction efficiency above 78.31%,we have successfully deep-routed 4.69 Tbit-s^(-1)quadrature phase-shift keying(QPSK)signals carried by four multiplexed OAM channels,with a bit error rate below 10^(-6).These results underscore the efficacy of our routing strategy and its promising prospects for practical applications.展开更多
We propose a quantum Otto engine operating through a cycle of two isochoric processes,where the working substance interacts with a single-mode radiation field,and two unitary strokes,during which the working substance...We propose a quantum Otto engine operating through a cycle of two isochoric processes,where the working substance interacts with a single-mode radiation field,and two unitary strokes,during which the working substance is decoupled from the field.We investigate the influence of quantum superposition and quantum internal friction on the engine's power output and efficiency,demonstrating that these quantum effects enhance both performance metrics.While these enhancements are accompanied by increased power fluctuations,we show that such fluctuations can be effectively mitigated through careful selection of control parameters.Our results reveal that the proposed quantum Otto engine can achieve performance regimes that are thermally inconceivable in classical systems,including surpassing the Otto efficiency limit and attaining 100%efficiency with nonzero power output.展开更多
In this work,we investigate disordered Dirac fermions from the perspective of quantum entanglement,which provides a different angle compared to the ordinary perturbative renormalization group(RG)analysis.We consider D...In this work,we investigate disordered Dirac fermions from the perspective of quantum entanglement,which provides a different angle compared to the ordinary perturbative renormalization group(RG)analysis.We consider Dirac fermions subjected to random hopping and random flux,which respectively fall into the chiral Gaussian orthogonal ensemble(cGOE)and chiral Gaussian unitary ensemble(cGUE)universality classes.Existing studies based on perturbative calculations suggest that both types of randomness are marginal.Here,through numerical simulations of the corresponding lattice models,we find that these two different types of randomness exhibit distinct entanglement features,signaling completely different properties in contrast to the perturbative RG analysis.In particular,although the entropy area-law is generally held for both types of randomness,we identify that the subleading term of the entanglement entropy is enhanced by random flux but not by random hopping.This subleading term is known as the entropic F-function in the clean limit without disorder.Our observations indicate that disordered theories in cGOE and cGUE are essentially different,which recalls careful analysis on the RG calculations.展开更多
In this paper,a method for designing supermassive sparse phased arrays(SMSPAs)known as the unitary modified matrix enhancement and matrix pencil(UMMEMP)method is proposed.In this method,an eigenvalue pairing method,wh...In this paper,a method for designing supermassive sparse phased arrays(SMSPAs)known as the unitary modified matrix enhancement and matrix pencil(UMMEMP)method is proposed.In this method,an eigenvalue pairing method,which is inspired by the modified MEMP,effectively pairs the repeated eigenvalues intractable in the unitary matrix pencil method,and it is more effective in determining the locations of elements in the sparse array.Three numerical examples and a full-wave validation are presented to demonstrate the effectiveness of the method,implemented via SMSPA,in achieving low sidelobe level wide-angle scanning radiation patterns,circular flattop radiation patterns,and ultra wide-angle scanning radiation patterns.展开更多
The performance loss of an approximately 3 dB signal-to-noise ratio is always paid with conventional differential detection compared to the related coherent detection. A new detection scheme consisting of two steps is...The performance loss of an approximately 3 dB signal-to-noise ratio is always paid with conventional differential detection compared to the related coherent detection. A new detection scheme consisting of two steps is proposed for the differential unitary space-time modulation （DUSTM） system. In the first step, the data sequence is estimated by conventional unitary space-time demodulation （DUSTD） and differentially encoded again to produce an initial estimate of the transmitted symbol stream. In the second step, the initial estimate of the symbol stream is utilized to initialize an expectation maximization （EM）-based iterative detector. In each iteration, the most recent detected symbol stream is employed to estimate the channel, which is then used to implement coherent sequence detection to refine the symbol stream. Simulation results show that the proposed detection scheme performs much better than the conventional DUSTD after several iterations.展开更多
Traditional air conditioner used to be in local control mode. However, with the development of modern information technology, the control of air conditioner will have to support many more functions. As a first step ...Traditional air conditioner used to be in local control mode. However, with the development of modern information technology, the control of air conditioner will have to support many more functions. As a first step in such a development, we have implemented a remote monitoring system of unitary air conditioners, using the manufacturing message specification (MMS). MMS is an OSI application protocol designed for the remote control and monitoring of real devices. The functions supported are those that an operator would do normally at the console of the unitary air conditioner. Due to the accomplishment of UMCS (Unitary air conditioner MMS Control System), there will be a leap of the application of MMS and the control technology of unitary air conditioner.展开更多
Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence o...Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence of and the expression for the generally unitary solution of the system are derived.展开更多
Different from the Hermitian case, non-Hermitian(NH) systems have novel properties and strongly relate to open and dissipative quantum systems. In this work, we investigate how to simulate τ-anti-pseudo-Hermitian sys...Different from the Hermitian case, non-Hermitian(NH) systems have novel properties and strongly relate to open and dissipative quantum systems. In this work, we investigate how to simulate τ-anti-pseudo-Hermitian systems in a Hermitian quantum device using linear combinations of unitaries and duality quantum algorithm. Specifying the τ to time-reversal(T) and parity-time-reversal(PT) operators, we construct the two NH two-level systems, design quantum circuits including three qubits, and decide the quantum gates explicitly in detail. We also calculate the success probabilities of the simulation.Experimental implementation can be expected in small quantum simulator.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11401256,11801219,11501249,11871342)the Scientific Research Fund of Zhejiang Provincial Education Department(No.Y202249575)the Zhejiang Provincial Natural Science Foundation of China(No.LQ13A010016)。
文摘The authors show that ifΘ=(θ_(jk))is a 3×3 totally irrational real skewsymmetric matrix,whereθ_(jk)∈[0,1)for j,k=1,2,3,then for anyε>0,there existsδ>0 satisfying the following:For any unital C^(*)-algebra A with the cancellation property,strict comparison and nonempty tracial state space,any four unitaries u1,u2,u3,w∈A such that(1)■,wujw-1=uj-1,w2=1A for j,k=1,2,3;(2)τ(aw)=0 and■for all n∈N,all a∈C^(*)(u1,u2,u3),j,k=1,2,3 and all tracial statesτon A,where C^(*)(u1,u2,u3)is the C^(*)-subalgebra generated by u1,u2 and u3,there exists a 4-tuple of unitaries■in A such that■and■for j,k=1,2,3.The above conclusion is also called that the rotation relations of three unitaries with the flip action is stable under the above conditions.
文摘The relation between conflict and governance has been dominated by type of government rather than by system of government.With increasing conflict in countries with ethnic and religious diversity,the debate has gradually shifted to understand better the link between conflict and system of government.There is a growing evidence that suggests federal system performs better than unitary system in managing diversity and reducing conflict.Decentralization is even seen to be more effective than federal system not only in managing diversity and reducing conflict but also in delivering public goods.This article provides an account of evolution of system of government in South Sudan.It finds a clear association of centralized unitary system with violent conflict and a relative peace during period of decentralized government or federal system.A decentralized federal system may be appropriate for South Sudan in managing diversity and mitigating conflict.Despite the popular demand by their citizens for a federal system to manage diversity and reduce violent conflict,the ruling elites in the post-independent South Sudan adopted instead an autocratic centralized unitary system that contributed among other factors to the persistent violent conflicts,erosion of social cohesion,and rising mistrust between state and citizens and between and among the communities of South Sudan.
基金Supported by NSFC(Nos.12361028,11761057)Science Foundation of Jiangxi Education Department(Nos.GJJ202302,GJJ202303,GJJ202319).
文摘We give a new result on the construction of K-frame generators for unitary systems by using the pseudo-inverses of involved operators,which provides an improvement to one known result on this topic.We also introduce the concept of K-woven generators for unitary systems,by means of which we investigate the weaving properties of K-frame generators for unitary systems.
基金supported by the National Natural Science Foundation of China(11931009,12271495,11971450,and 12071449)Anhui Initiative in Quantum Information Technologies(AHY150200)the Project of Stable Support for Youth Team in Basic Research Field,Chinese Academy of Sciences(YSBR-001).
文摘On a compact Riemann surface with finite punctures P_(1),…P_(k),we define toric curves as multivalued,totallyunramified holomorphic maps to P^(n)with monodromy in a maximal torus of PSU(n+1).Toric solutions to SU(n+1)Todasystems on X\{P_(1);…;P_(k)}are recognized by the associated toric curves in.We introduce character n-ensembles as-tuples of meromorphic one-forms with simple poles and purely imaginary periods,generating toric curves on minus finitelymany points.On X,we establish a correspondence between character-ensembles and toric solutions to the SU(n+1)system with finitely many cone singularities.Our approach not only broadens seminal solutions with two conesingularities on the Riemann sphere,as classified by Jost-Wang(Int.Math.Res.Not.,2002,(6):277-290)andLin-Wei-Ye(Invent.Math.,2012,190(1):169-207),but also advances beyond the limits of Lin-Yang-Zhong’s existencetheorems(J.Differential Geom.,2020,114(2):337-391)by introducing a new solution class.
基金the National Natural Science Foundation of China(62271322)the Guangdong Basic and Applied Basic Research Foundation(2022A1515011003 and 2023A1515030152)the Shenzhen Science and Technology Program(JCYJ20210324095610027 and JCYJ20210324095611030).
文摘Optical orbital angular momentum(OAM)mode multiplexing has emerged as a promising technique for boosting communication capacity.However,most existing studies have concentrated on channel(de)-multiplexing,overlooking the critical aspect of channel routing.This challenge involves the reallocation of multiplexed OAM modes across both spatial and temporal domains—a vital step for developing versatile communication networks.To address this gap,we introduce a novel approach based on the time evolution of OAM modes,utilizing the orthogonal conversion and diffractive modulation capabilities of unitary transformations.This approach facilitates high-dimensional orthogonal transformations of OAM mode vectors,altering both the propagation direction and the spatial location.Using Fresnel diffraction matrices as unitary operators,it manipulates the spatial locations of light beams during transmission,breaking the propagation invariance and enabling temporal evolution.As a demonstration,we have experimentally implemented the deep routing of four OAM modes within two distinct time sequences.Achieving an average diffraction efficiency above 78.31%,we have successfully deep-routed 4.69 Tbit-s^(-1)quadrature phase-shift keying(QPSK)signals carried by four multiplexed OAM channels,with a bit error rate below 10^(-6).These results underscore the efficacy of our routing strategy and its promising prospects for practical applications.
基金supported by the National Natural Science Foundation of China(Grant No.12465009)support from the Major Program of Jiangxi Provincial Natural Science Foundation,China(Grant No.20224ACB201007)。
文摘We propose a quantum Otto engine operating through a cycle of two isochoric processes,where the working substance interacts with a single-mode radiation field,and two unitary strokes,during which the working substance is decoupled from the field.We investigate the influence of quantum superposition and quantum internal friction on the engine's power output and efficiency,demonstrating that these quantum effects enhance both performance metrics.While these enhancements are accompanied by increased power fluctuations,we show that such fluctuations can be effectively mitigated through careful selection of control parameters.Our results reveal that the proposed quantum Otto engine can achieve performance regimes that are thermally inconceivable in classical systems,including surpassing the Otto efficiency limit and attaining 100%efficiency with nonzero power output.
基金supported by the National Key Research and Development Program(Grant No.2022YFA1402204)the National Natural Science Foundation[Grant Nos.22373095(QL),52471020(WC),and 12474144(WZ)]+2 种基金the Innovation Program for Quantum Science and Technology[Grant No.2021ZD0303306(QL)]the Fundamental Research Funds for the Central Universities[Grant No.JZ2025HGQA0310(WC)]the Science Research Foundation for High-Level Talents of Anhui University of Science and Technology[Grant No.YJ20240002(WL)].
文摘In this work,we investigate disordered Dirac fermions from the perspective of quantum entanglement,which provides a different angle compared to the ordinary perturbative renormalization group(RG)analysis.We consider Dirac fermions subjected to random hopping and random flux,which respectively fall into the chiral Gaussian orthogonal ensemble(cGOE)and chiral Gaussian unitary ensemble(cGUE)universality classes.Existing studies based on perturbative calculations suggest that both types of randomness are marginal.Here,through numerical simulations of the corresponding lattice models,we find that these two different types of randomness exhibit distinct entanglement features,signaling completely different properties in contrast to the perturbative RG analysis.In particular,although the entropy area-law is generally held for both types of randomness,we identify that the subleading term of the entanglement entropy is enhanced by random flux but not by random hopping.This subleading term is known as the entropic F-function in the clean limit without disorder.Our observations indicate that disordered theories in cGOE and cGUE are essentially different,which recalls careful analysis on the RG calculations.
文摘In this paper,a method for designing supermassive sparse phased arrays(SMSPAs)known as the unitary modified matrix enhancement and matrix pencil(UMMEMP)method is proposed.In this method,an eigenvalue pairing method,which is inspired by the modified MEMP,effectively pairs the repeated eigenvalues intractable in the unitary matrix pencil method,and it is more effective in determining the locations of elements in the sparse array.Three numerical examples and a full-wave validation are presented to demonstrate the effectiveness of the method,implemented via SMSPA,in achieving low sidelobe level wide-angle scanning radiation patterns,circular flattop radiation patterns,and ultra wide-angle scanning radiation patterns.
基金The National Natural Science Foundation of China(No60572072,60496311)the National High Technology Research and Development Program of China (863Program) (No2006AA01Z264)+1 种基金the National Basic Research Program of China (973Program) (No2007CB310603)the PhD Programs Foundation of Ministry of Educa-tion of China (No20060286016)
文摘The performance loss of an approximately 3 dB signal-to-noise ratio is always paid with conventional differential detection compared to the related coherent detection. A new detection scheme consisting of two steps is proposed for the differential unitary space-time modulation （DUSTM） system. In the first step, the data sequence is estimated by conventional unitary space-time demodulation （DUSTD） and differentially encoded again to produce an initial estimate of the transmitted symbol stream. In the second step, the initial estimate of the symbol stream is utilized to initialize an expectation maximization （EM）-based iterative detector. In each iteration, the most recent detected symbol stream is employed to estimate the channel, which is then used to implement coherent sequence detection to refine the symbol stream. Simulation results show that the proposed detection scheme performs much better than the conventional DUSTD after several iterations.
文摘Traditional air conditioner used to be in local control mode. However, with the development of modern information technology, the control of air conditioner will have to support many more functions. As a first step in such a development, we have implemented a remote monitoring system of unitary air conditioners, using the manufacturing message specification (MMS). MMS is an OSI application protocol designed for the remote control and monitoring of real devices. The functions supported are those that an operator would do normally at the console of the unitary air conditioner. Due to the accomplishment of UMCS (Unitary air conditioner MMS Control System), there will be a leap of the application of MMS and the control technology of unitary air conditioner.
文摘Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence of and the expression for the generally unitary solution of the system are derived.
基金funded by the National Natural Science Foundation of China (Grant No. 12175002)Beijing Natural Science Foundation (Grant No. 1222020)NCUT Talents Project and Special Fund。
文摘Different from the Hermitian case, non-Hermitian(NH) systems have novel properties and strongly relate to open and dissipative quantum systems. In this work, we investigate how to simulate τ-anti-pseudo-Hermitian systems in a Hermitian quantum device using linear combinations of unitaries and duality quantum algorithm. Specifying the τ to time-reversal(T) and parity-time-reversal(PT) operators, we construct the two NH two-level systems, design quantum circuits including three qubits, and decide the quantum gates explicitly in detail. We also calculate the success probabilities of the simulation.Experimental implementation can be expected in small quantum simulator.
