The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattic...The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattice constant ratio of 1:2 as an example. For the symmetric nearest-neighbor intra-chain hopping two-leg ladder, the inversion symmetry protected topological insulator phase with two degenerate topological edge states appears. When the inversion symmetry is broken, the topological insulators with one or two topological edge states of different energies and topological metals with edge states embedded in the bulk states could emerge depending on the filling factor. The topological origin of these topological states in the two-leg ladders is the topological properties of the Chern insulators and Chern metals. According to the arrangement of two trivial quantum wires, we construct two types of three-leg ladders. Each type of the three-leg ladder could be divided into one trivial subspace and one topological nontrivial subspace by unitary transformation. The topological nontrivial subspace corresponds to the effective two-leg ladder model. As the filling factor changes, the system could be in topological insulators or topological metals phases. When the two-leg ladder is constructed by two trivial quantum wires with a lattice constant ratio of 1:3 and 2:3, the system could also realize rich topological states such as the topological insulators and topological metals with the topological edge states. These rich topological states in the two-leg and three-leg ladders could be confirmed by current experimental techniques.展开更多
The exploration of topological phases remains a cutting-edge research frontier,driven by their promising potential for next-generation electronic and quantum technologies.In this work,we employ first-principles calcul...The exploration of topological phases remains a cutting-edge research frontier,driven by their promising potential for next-generation electronic and quantum technologies.In this work,we employ first-principles calculations and tightbinding modeling to systematically investigate the topological properties of freestanding two-dimensional(2D)honeycomb Bi,HgTe,and Al_(2)O_(3)(0001)-supported HgTe.Remarkably,all three systems exhibit coexistence of intrinsic first-and higher-order topological insulator states,induced by spin-orbit coupling(SOC).These states manifest as topologically protected gapless edge states in one-dimensional(1D)nanoribbons and symmetry-related corner states in zero-dimensional(0D)nanoflakes.Furthermore,fractional electron charges may accumulate at the corners of armchair-edged nanoflakes.Among these materials,HgTe/Al_(2)O_(3)(0001)is particularly promising due to its experimentally feasible atomic configuration and low-energy corner states.Our findings highlight the importance of exploring higher-order topological phases in quantum spin Hall insulators and pave the way for new possibilities in device applications.展开更多
We theoretically investigate the electronic structure of cylindrical magnetic topological insulator quantum wires in MnBi_(2)Te_(4).Our study reveals the emergence of topological surface states in the ferromagnetic ph...We theoretically investigate the electronic structure of cylindrical magnetic topological insulator quantum wires in MnBi_(2)Te_(4).Our study reveals the emergence of topological surface states in the ferromagnetic phase,characterized by spin-polarized subbands resulting from intrinsic magnetization.In the antiferromagnetic phase,we identify the coexistence of three distinct types of topological states,encompassing both surface states and central states.展开更多
The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of pla...The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of plane waves used for expansion on the stability of energy eigenvalues is examined.For practical calculation,it should choose the period large sufficiently to ensure the envelope functions vanish at the boundary and the number of plane waves large enough to ensure the energy eigenvalues keep unchanged within a prescribed range.展开更多
A flexure hinge is a major component in designing compliant mechanisms that o ers unique possibilities in a wide range of application fields in which high positioning accuracy is required. Although various flexure hin...A flexure hinge is a major component in designing compliant mechanisms that o ers unique possibilities in a wide range of application fields in which high positioning accuracy is required. Although various flexure hinges with di erent configurations have been successively proposed, they are often designed based on designers' experiences and inspirations. This study presents a systematic method for topological optimization of flexure hinges by using the level set method. Optimization formulations are developed by considering the functional requirements and geometrical constraints of flexure hinges. The functional requirements are first constructed by maximizing the compliance in the desired direction while minimizing the compliances in the other directions. The weighting sum method is used to construct an objective function in which a self-adjust method is used to set the weighting factors. A constraint on the symmetry of the obtained configuration is developed. Several numerical examples are presented to demonstrate the validity of the proposed method. The obtained results reveal that the design of a flexure hinge starting from the topology level can yield more choices for compliant mechanism design and obtain better designs that achieve higher performance.展开更多
Based on a level set model, a topology optimization method has been suggestedrecently. It uses a level set to express the moving structural boundary, which can flexibly handlecomplex topological changes. By combining ...Based on a level set model, a topology optimization method has been suggestedrecently. It uses a level set to express the moving structural boundary, which can flexibly handlecomplex topological changes. By combining vector level set models with gradient projectiontechnology, the level set method for topological optimization is extended to a topologicaloptimization problem with multi-constraints, multi-materials and multi-load cases. Meanwhile, anappropriate nonlinear speed, mapping is established in the tangential space of the activeconstraints for a fast convergence. Then the method is applied to structure designs, mechanism andmaterial designs by a number of benchmark examples. Finally, in order to further improvecomputational efficiency and overcome the difficulty that the level set method cannot generate newmaterial interfaces during the optimization process, the topological derivative analysis isincorporated into the level set method for topological optimization, and a topological derivativeand level set algorithm for topological optimization is proposed.展开更多
A two-dimensional （2D） full band self-consistent ensemble Monte Carlo （MC） method for solving the quantum Boltzmann equation, including collision broadening and quantum potential corrections, is developed to exten...A two-dimensional （2D） full band self-consistent ensemble Monte Carlo （MC） method for solving the quantum Boltzmann equation, including collision broadening and quantum potential corrections, is developed to extend the MC method to the study of nano-scale semiconductor devices with obvious quantum mechanical （QM） effects. The quantum effects both in real space and momentum space in nano-scale semiconductor devices can be simulated. The effective mobility in the inversion layer of n and p channel MOSFET is simulated and compared with experimental data to verify this method. With this method 50nm ultra thin body silicon on insulator MOSFET are simulated. Results indicate that this method can be used to simulate the 2D QM effects in semiconductor devices including tunnelling effect.展开更多
In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First,...In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First, the density matrix interested in quantum system is transferred to vector formation.Then, in order to obtain a controller with higher accuracy and faster convergence rate, a Lyapunov function based on the matrix logarithm function is designed. After that, a procedure for the controller design is derived based on the Lyapunov stability theorem. Finally, the numerical simulation experiments for an amplitude damping Markovian open quantum system are performed to prepare the desired quantum gate. The simulation results show that the preparation of Hadamard gate based on the proposed control laws can achieve the fidelity up to 0.9985 for the different coupling strengths.展开更多
The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eige...The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.展开更多
Employing the Pekeris-type approximation to deal with the pseudo-centrifugal term,we analytically study the pseudospin symmetry of a Dirac nucleon subjected to equal scalar and vector modified Rosen-Morse potential in...Employing the Pekeris-type approximation to deal with the pseudo-centrifugal term,we analytically study the pseudospin symmetry of a Dirac nucleon subjected to equal scalar and vector modified Rosen-Morse potential including the spin-orbit coupling term by using the Nikiforov-Uvarov method and supersymmetric quantum mechanics approach.The complex eigenvalue equation and the total normalized wave functions expressed in terms of Jacobi polynomial with arbitrary spin-orbit coupling quantum number k are presented under the condition of pseudospin symmetry.The eigenvalue equations for both methods reproduce the same result to affirm the mathematical accuracy of analytical calculations.The numerical solutions obtained for different adjustable parameters produce degeneracies for some quantum number.展开更多
Fixture locating layout has a direct and influential impact on aeronautical thin-walled component(ATWC)manufacturing quality.The purpose is to develop a topological optimization method for ATWC fixture locating layout...Fixture locating layout has a direct and influential impact on aeronautical thin-walled component(ATWC)manufacturing quality.The purpose is to develop a topological optimization method for ATWC fixture locating layout to minimize the manufacturing deformation.Firstly,a topological optimization model that takes the stiffness of ATWC as the objective function and the volume of the locating structure as the constraint is established.Secondly,ATWC and the locating structure are regarded as an integrated entity,and the variable-density method based topological optimization approach is adopted for the optimization of the locating structure using ABAQUS topology optimization module(ATOM).Thirdly,through a subsequent model reconstruction referring to the obtained topological structure,the optimal fixture locating layout is achieved.Finally,a case study is conducted to verify the proposed method and the comparison results with firefly algorithm(FA)coupled with finite element analysis(FEA)indicate that the number and positions of the locators for ATWC can be optimized simultaneously and successfully by the proposed topological optimization model.展开更多
The anomalous dimensions of the quantum fields are the Hausdorff dimensiongrad. The present candidate of the renormalization constant is the generalized Cantor discontinuum. The Hausdorff dimensiongrad of the Minkowsk...The anomalous dimensions of the quantum fields are the Hausdorff dimensiongrad. The present candidate of the renormalization constant is the generalized Cantor discontinuum. The Hausdorff dimensiongrad of the Minkowski space time is based upon the point set with σ-length on light cone.展开更多
Projection-based embedded discrete fracture model(pEDFM)is an effective numerical model to handle the flow in fractured reservoirs,with high efficiency and strong generalization of flow models.However,this paper point...Projection-based embedded discrete fracture model(pEDFM)is an effective numerical model to handle the flow in fractured reservoirs,with high efficiency and strong generalization of flow models.However,this paper points out that pEDFM fails to handle flow barriers in most cases,and identifies the physical projection configuration of fractures is a key step in pEDFM.This paper presents and proves the equivalence theorem,which explains the geometric nature of physical projection configurations of fractures,that is,the projection configuration of a fracture being physical is equivalent to it being topologically homeomorphic to the fracture,by analyzing the essence of pEDFM.Physical projection configurations of fractures may be rigorously established based on this theorem,allowing pEDFM to obtain physical numerical results for many flow models,particularly those with flow barriers.Furthermore,a natural idea emerges of employing flow barriers to flexibly‘cut’the formation to quickly handle the flow problems in the formation with complex geological conditions,and several numerical examples are implemented to test this idea and application of the improved pEDFM.展开更多
The authors study the covering rough sets by topological methods. They combine the covering rough sets and topological spaces by means of defining some new types of spaces called covering rough topological (CRT) space...The authors study the covering rough sets by topological methods. They combine the covering rough sets and topological spaces by means of defining some new types of spaces called covering rough topological (CRT) spaces based on neighbourhoods or complementary neighbourhoods. As the separation axioms play a fundamental role in general topology, they introduce all these axioms into covering rough set theories and thoroughly study the equivalent conditions for every separation axiom in several CRT spaces. They also investigate the relationships between the separation axioms in these special spaces and reveal these relationships through diagrams in different CRT spaces.展开更多
We utilize two different theories to prove that cosmic dark energy density is the complimentary Legendre transformation of ordinary energy and vice versa as given by E(dark) = mc2 (21/22) and E(ordinary) = mc2/22. The...We utilize two different theories to prove that cosmic dark energy density is the complimentary Legendre transformation of ordinary energy and vice versa as given by E(dark) = mc2 (21/22) and E(ordinary) = mc2/22. The first theory used is based on G ‘t Hooft’s remarkably simple renormalization procedure in which a neat mathematical maneuver is introduced via the dimensionality of our four dimensional spacetime. Thus, ‘t Hooft used instead of D = 4 and then took at the end of an intricate and subtle computation the limit to obtain the result while avoiding various problems including the pole singularity at D = 4. Here and in contradistinction to the classical form of dimensional and renormalization we set and do not take the limit where and is the theoretically and experimentally well established Hardy’s generic quantum entanglement. At the end we see that the dark energy density is simply the ratio of and the smooth disentangled D = 4, i.e. (dark) = (4 -k)/4 = 3.8196011/4 = 0.9549150275. Consequently where we have ignored the fine structure details by rounding 21 + k to 21 and 22 + k to 22 in a manner not that much different from of the original form of dimensional regularization theory. The result is subsequently validated by another equally ingenious approach due mainly to E. Witten and his school of topological quantum field theory. We notice that in that theory the local degrees of freedom are zero. Therefore, we are dealing essentially with pure gravity where are the degrees of freedom and is the corresponding dimension. The results and the conclusion of the paper are summarized in Figure 1-3, Table 1 and Flow Chart 1.展开更多
Considering the ocean water＇s optical attenuation and the roughness of the sea surface, we analyze the security of continuous-variable （CV） quantum key distribution （QKD） based Mr-to-water channel. The effects of...Considering the ocean water＇s optical attenuation and the roughness of the sea surface, we analyze the security of continuous-variable （CV） quantum key distribution （QKD） based Mr-to-water channel. The effects of the absorp- tion and scattering on the transmittance of underwater quantum channel and the maximum secure transmission distance are studied. Considering the roughness of the sea surface, we simulate the performance bounds of CV QKD with different wind speeds using the Monte Carlo method. The results show that even if the secret key rate gradually reduces as the wind speed increases, the maximum transmission distance will not be affected obviously. Compared to the works regarding short-distance underwater optical communication, our research represents a significant step towards establishing secure communication between air platform and submarine vehicle.展开更多
Quantum Hall effect （QHE）, as a class of quantum phenomena that occur in macroscopic scale, is one of the most important topics in condensed matter physics. It has long been expected that QHE may occur without Landa...Quantum Hall effect （QHE）, as a class of quantum phenomena that occur in macroscopic scale, is one of the most important topics in condensed matter physics. It has long been expected that QHE may occur without Landau levels so that neither external magnetic field nor high sample mobility is required for its study and application, Such a QHE free of Landau levels, can appear in topological insulators （TIs） with ferromagnetism as the quantized version of the anomalous Hall effect, i.e., quantum anomalous Hall （QAH） effect. Here we review our recent work on experimental realization of the QAH effect in magnetically doped TIs. With molecular beam epitaxy, we prepare thin films of Cr-doped （Bi,Sb）2Te3 TIs with well- controlled chemical potential and long-range ferromagnetic order that can survive the insulating phase. In such thin films, we eventually observed the quantization of the Hall resistance at h/e2 at zero field, accompanied by a considerable drop in the longitudinal resistance. Under a strong magnetic field, the longitudinal resistance vanishes, whereas the Hall resistance remains at the quantized value. The realization of the QAH effect provides a foundation for many other novel quantum phenomena predicted in TIs, and opens a route to practical applications of quantum Hall physics in low-power-consumption electronics.展开更多
The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number Cs for energy-bands of trilayer graphene having the essenc...The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number Cs for energy-bands of trilayer graphene having the essence of intrinsic spin-orbit coupling is analytically calculated. We find that for each valley and spin, Cs is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states, consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin-orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin-orbit （RSO） interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin-orbit coupling, while the other two layers have zero intrinsic spin-orbit coupling. Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.展开更多
We analyze the reading and initialization of a topological qubit encoded by Majorana fermions in one-dimensional semiconducting nanowires, weakly coupled to a single level quantum dot （QD）. It is shown that when the...We analyze the reading and initialization of a topological qubit encoded by Majorana fermions in one-dimensional semiconducting nanowires, weakly coupled to a single level quantum dot （QD）. It is shown that when the Majorana fermions are fused by tuning gate voltage, the topological qubit can be read out directly through the occupation of the QD in an energy window. The initialization of the qubit can also be realized via adjusting the gate voltage on the QD, with the total fermion parity conserved. As a result, both reading and initialization processes can be achieved in an all-electrical way.展开更多
In this work, we discuss the topological transformation of quantum dynamics by showing the wave dynamics of a quantum particle on different types of topological structures in various dimensions from the fundamental po...In this work, we discuss the topological transformation of quantum dynamics by showing the wave dynamics of a quantum particle on different types of topological structures in various dimensions from the fundamental polygons of the corresponding universal covering spaces. This is not the view from different perspectives of an observer who simply uses different coordinate systems to describe the same physical phenomenon but rather possible geometric and topological structures that quantum particles are endowed with when they are identified with differentiable manifolds that are embedded or immersed in Euclidean spaces of higher dimension. We present our discussions in the form of Bohr model in one, two and three dimensions using linear wave equations. In one dimension, the fundamental polygon is an interval and the universal covering space is the straight line and in this case the standing wave on a finite string is transformed into the standing wave on a circle which can be applied into the Bohr model of the hydrogen atom. In two dimensions, the fundamental polygon is a square and the universal covering space is the plane and in this case, the standing wave on the square is transformed into the standing wave on different surfaces that can be formed by gluing opposite sides of the square, which include a 2-sphere, a 2-torus, a Klein bottle and a projective plane. In three dimensions, the fundamental polygon is a cube and the universal covering space is the three-dimensional Euclidean space. It is shown that a 3-torus and the manifold K?× S1?defined as the product of a Klein bottle and a circle can be constructed by gluing opposite faces of a cube. Therefore, in three-dimensions, the standing wave on a cube is transformed into the standing wave on a 3-torus or on the manifold K?× S1. We also suggest that the mathematical degeneracy may play an important role in quantum dynamics and be associated with the concept of wavefunction collapse in quantum mechanics.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12074101 and 11604081)sponsored by the Natural Science Foundation of Henan Province, China (Grant No. 212300410040)。
文摘The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattice constant ratio of 1:2 as an example. For the symmetric nearest-neighbor intra-chain hopping two-leg ladder, the inversion symmetry protected topological insulator phase with two degenerate topological edge states appears. When the inversion symmetry is broken, the topological insulators with one or two topological edge states of different energies and topological metals with edge states embedded in the bulk states could emerge depending on the filling factor. The topological origin of these topological states in the two-leg ladders is the topological properties of the Chern insulators and Chern metals. According to the arrangement of two trivial quantum wires, we construct two types of three-leg ladders. Each type of the three-leg ladder could be divided into one trivial subspace and one topological nontrivial subspace by unitary transformation. The topological nontrivial subspace corresponds to the effective two-leg ladder model. As the filling factor changes, the system could be in topological insulators or topological metals phases. When the two-leg ladder is constructed by two trivial quantum wires with a lattice constant ratio of 1:3 and 2:3, the system could also realize rich topological states such as the topological insulators and topological metals with the topological edge states. These rich topological states in the two-leg and three-leg ladders could be confirmed by current experimental techniques.
基金supported by the Program for Science and Technology Innovation Team in Zhejiang Province,China(Grant No.2021R01004)the Six Talent Peaks Project of Jiangsu Province,China(Grant No.2019-XCL-081)the Startup Funding of Ningbo University and Yongjiang Recruitment Project(Grant No.432200942).
文摘The exploration of topological phases remains a cutting-edge research frontier,driven by their promising potential for next-generation electronic and quantum technologies.In this work,we employ first-principles calculations and tightbinding modeling to systematically investigate the topological properties of freestanding two-dimensional(2D)honeycomb Bi,HgTe,and Al_(2)O_(3)(0001)-supported HgTe.Remarkably,all three systems exhibit coexistence of intrinsic first-and higher-order topological insulator states,induced by spin-orbit coupling(SOC).These states manifest as topologically protected gapless edge states in one-dimensional(1D)nanoribbons and symmetry-related corner states in zero-dimensional(0D)nanoflakes.Furthermore,fractional electron charges may accumulate at the corners of armchair-edged nanoflakes.Among these materials,HgTe/Al_(2)O_(3)(0001)is particularly promising due to its experimentally feasible atomic configuration and low-energy corner states.Our findings highlight the importance of exploring higher-order topological phases in quantum spin Hall insulators and pave the way for new possibilities in device applications.
基金Project sponsored by the Natural Science Foundation of Chongqing,China(Grant No.CSTB2024NSCQMSX0736)the Special Project of Chongqing Technology Innovation and Application Development(Major Project)(Grant No.CSTB2024TIAD-STX0035)the Research Foundation of Institute for Advanced Sciences of CQUPT(Grant No.E011A2022328)。
文摘We theoretically investigate the electronic structure of cylindrical magnetic topological insulator quantum wires in MnBi_(2)Te_(4).Our study reveals the emergence of topological surface states in the ferromagnetic phase,characterized by spin-polarized subbands resulting from intrinsic magnetization.In the antiferromagnetic phase,we identify the coexistence of three distinct types of topological states,encompassing both surface states and central states.
文摘The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of plane waves used for expansion on the stability of energy eigenvalues is examined.For practical calculation,it should choose the period large sufficiently to ensure the envelope functions vanish at the boundary and the number of plane waves large enough to ensure the energy eigenvalues keep unchanged within a prescribed range.
基金Supported by National Natural Science Foundation of China(Grant Nos.51605166,51820105007)Fundamental Research Funds for the Central Universities of China
文摘A flexure hinge is a major component in designing compliant mechanisms that o ers unique possibilities in a wide range of application fields in which high positioning accuracy is required. Although various flexure hinges with di erent configurations have been successively proposed, they are often designed based on designers' experiences and inspirations. This study presents a systematic method for topological optimization of flexure hinges by using the level set method. Optimization formulations are developed by considering the functional requirements and geometrical constraints of flexure hinges. The functional requirements are first constructed by maximizing the compliance in the desired direction while minimizing the compliances in the other directions. The weighting sum method is used to construct an objective function in which a self-adjust method is used to set the weighting factors. A constraint on the symmetry of the obtained configuration is developed. Several numerical examples are presented to demonstrate the validity of the proposed method. The obtained results reveal that the design of a flexure hinge starting from the topology level can yield more choices for compliant mechanism design and obtain better designs that achieve higher performance.
基金This project is supported by National Natural Science Foundation of China(No.598005001, No.10332010) and Key Science and Technology Research Project of Ministry of Education (No.104060).
文摘Based on a level set model, a topology optimization method has been suggestedrecently. It uses a level set to express the moving structural boundary, which can flexibly handlecomplex topological changes. By combining vector level set models with gradient projectiontechnology, the level set method for topological optimization is extended to a topologicaloptimization problem with multi-constraints, multi-materials and multi-load cases. Meanwhile, anappropriate nonlinear speed, mapping is established in the tangential space of the activeconstraints for a fast convergence. Then the method is applied to structure designs, mechanism andmaterial designs by a number of benchmark examples. Finally, in order to further improvecomputational efficiency and overcome the difficulty that the level set method cannot generate newmaterial interfaces during the optimization process, the topological derivative analysis isincorporated into the level set method for topological optimization, and a topological derivativeand level set algorithm for topological optimization is proposed.
基金Project supported by the Special Foundation for State Major Basic Research Program of China （Grant No G2000035602） and the National Natural Science Foundation of China （Grant No 90307006）.
文摘A two-dimensional （2D） full band self-consistent ensemble Monte Carlo （MC） method for solving the quantum Boltzmann equation, including collision broadening and quantum potential corrections, is developed to extend the MC method to the study of nano-scale semiconductor devices with obvious quantum mechanical （QM） effects. The quantum effects both in real space and momentum space in nano-scale semiconductor devices can be simulated. The effective mobility in the inversion layer of n and p channel MOSFET is simulated and compared with experimental data to verify this method. With this method 50nm ultra thin body silicon on insulator MOSFET are simulated. Results indicate that this method can be used to simulate the 2D QM effects in semiconductor devices including tunnelling effect.
基金supported by National Natural Science Foundation of China(61573330)Chinese Academy of Sciences(CAS)the World Academy of Sciences(TWAS)
文摘In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First, the density matrix interested in quantum system is transferred to vector formation.Then, in order to obtain a controller with higher accuracy and faster convergence rate, a Lyapunov function based on the matrix logarithm function is designed. After that, a procedure for the controller design is derived based on the Lyapunov stability theorem. Finally, the numerical simulation experiments for an amplitude damping Markovian open quantum system are performed to prepare the desired quantum gate. The simulation results show that the preparation of Hadamard gate based on the proposed control laws can achieve the fidelity up to 0.9985 for the different coupling strengths.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10875018 and 10773002)
文摘The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.
文摘Employing the Pekeris-type approximation to deal with the pseudo-centrifugal term,we analytically study the pseudospin symmetry of a Dirac nucleon subjected to equal scalar and vector modified Rosen-Morse potential including the spin-orbit coupling term by using the Nikiforov-Uvarov method and supersymmetric quantum mechanics approach.The complex eigenvalue equation and the total normalized wave functions expressed in terms of Jacobi polynomial with arbitrary spin-orbit coupling quantum number k are presented under the condition of pseudospin symmetry.The eigenvalue equations for both methods reproduce the same result to affirm the mathematical accuracy of analytical calculations.The numerical solutions obtained for different adjustable parameters produce degeneracies for some quantum number.
基金supported by the National Natural Science Foundation of China(No.51375396)the Shaanxi Science and Technology Innovation Project Plan,China(No.2016KTCQ01-50)
文摘Fixture locating layout has a direct and influential impact on aeronautical thin-walled component(ATWC)manufacturing quality.The purpose is to develop a topological optimization method for ATWC fixture locating layout to minimize the manufacturing deformation.Firstly,a topological optimization model that takes the stiffness of ATWC as the objective function and the volume of the locating structure as the constraint is established.Secondly,ATWC and the locating structure are regarded as an integrated entity,and the variable-density method based topological optimization approach is adopted for the optimization of the locating structure using ABAQUS topology optimization module(ATOM).Thirdly,through a subsequent model reconstruction referring to the obtained topological structure,the optimal fixture locating layout is achieved.Finally,a case study is conducted to verify the proposed method and the comparison results with firefly algorithm(FA)coupled with finite element analysis(FEA)indicate that the number and positions of the locators for ATWC can be optimized simultaneously and successfully by the proposed topological optimization model.
文摘The anomalous dimensions of the quantum fields are the Hausdorff dimensiongrad. The present candidate of the renormalization constant is the generalized Cantor discontinuum. The Hausdorff dimensiongrad of the Minkowski space time is based upon the point set with σ-length on light cone.
基金supported by the National Natural Science Foundation of China(No.52104017)National Key Research and Development Program of China(Grant No.2019YFA0705501)State Center for Research and Development of Oil Shale Exploitation,and Cooperative Innovation Center of Unconventional Oil and Gas(Ministry of Education&Hubei Province),Yangtze University(No.UOG2020-17).
文摘Projection-based embedded discrete fracture model(pEDFM)is an effective numerical model to handle the flow in fractured reservoirs,with high efficiency and strong generalization of flow models.However,this paper points out that pEDFM fails to handle flow barriers in most cases,and identifies the physical projection configuration of fractures is a key step in pEDFM.This paper presents and proves the equivalence theorem,which explains the geometric nature of physical projection configurations of fractures,that is,the projection configuration of a fracture being physical is equivalent to it being topologically homeomorphic to the fracture,by analyzing the essence of pEDFM.Physical projection configurations of fractures may be rigorously established based on this theorem,allowing pEDFM to obtain physical numerical results for many flow models,particularly those with flow barriers.Furthermore,a natural idea emerges of employing flow barriers to flexibly‘cut’the formation to quickly handle the flow problems in the formation with complex geological conditions,and several numerical examples are implemented to test this idea and application of the improved pEDFM.
文摘The authors study the covering rough sets by topological methods. They combine the covering rough sets and topological spaces by means of defining some new types of spaces called covering rough topological (CRT) spaces based on neighbourhoods or complementary neighbourhoods. As the separation axioms play a fundamental role in general topology, they introduce all these axioms into covering rough set theories and thoroughly study the equivalent conditions for every separation axiom in several CRT spaces. They also investigate the relationships between the separation axioms in these special spaces and reveal these relationships through diagrams in different CRT spaces.
文摘We utilize two different theories to prove that cosmic dark energy density is the complimentary Legendre transformation of ordinary energy and vice versa as given by E(dark) = mc2 (21/22) and E(ordinary) = mc2/22. The first theory used is based on G ‘t Hooft’s remarkably simple renormalization procedure in which a neat mathematical maneuver is introduced via the dimensionality of our four dimensional spacetime. Thus, ‘t Hooft used instead of D = 4 and then took at the end of an intricate and subtle computation the limit to obtain the result while avoiding various problems including the pole singularity at D = 4. Here and in contradistinction to the classical form of dimensional and renormalization we set and do not take the limit where and is the theoretically and experimentally well established Hardy’s generic quantum entanglement. At the end we see that the dark energy density is simply the ratio of and the smooth disentangled D = 4, i.e. (dark) = (4 -k)/4 = 3.8196011/4 = 0.9549150275. Consequently where we have ignored the fine structure details by rounding 21 + k to 21 and 22 + k to 22 in a manner not that much different from of the original form of dimensional regularization theory. The result is subsequently validated by another equally ingenious approach due mainly to E. Witten and his school of topological quantum field theory. We notice that in that theory the local degrees of freedom are zero. Therefore, we are dealing essentially with pure gravity where are the degrees of freedom and is the corresponding dimension. The results and the conclusion of the paper are summarized in Figure 1-3, Table 1 and Flow Chart 1.
基金Supported by the National Natural Science Foundation of China under Grant No 61572529
文摘Considering the ocean water＇s optical attenuation and the roughness of the sea surface, we analyze the security of continuous-variable （CV） quantum key distribution （QKD） based Mr-to-water channel. The effects of the absorp- tion and scattering on the transmittance of underwater quantum channel and the maximum secure transmission distance are studied. Considering the roughness of the sea surface, we simulate the performance bounds of CV QKD with different wind speeds using the Monte Carlo method. The results show that even if the secret key rate gradually reduces as the wind speed increases, the maximum transmission distance will not be affected obviously. Compared to the works regarding short-distance underwater optical communication, our research represents a significant step towards establishing secure communication between air platform and submarine vehicle.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11174343 and 11134008)the National Basic Research Program of China(Grant Nos. 2013CB921702 and 2009CB929400)the Knowledge Innovation Program of the Chinese Academy of Sciences
文摘Quantum Hall effect （QHE）, as a class of quantum phenomena that occur in macroscopic scale, is one of the most important topics in condensed matter physics. It has long been expected that QHE may occur without Landau levels so that neither external magnetic field nor high sample mobility is required for its study and application, Such a QHE free of Landau levels, can appear in topological insulators （TIs） with ferromagnetism as the quantized version of the anomalous Hall effect, i.e., quantum anomalous Hall （QAH） effect. Here we review our recent work on experimental realization of the QAH effect in magnetically doped TIs. With molecular beam epitaxy, we prepare thin films of Cr-doped （Bi,Sb）2Te3 TIs with well- controlled chemical potential and long-range ferromagnetic order that can survive the insulating phase. In such thin films, we eventually observed the quantization of the Hall resistance at h/e2 at zero field, accompanied by a considerable drop in the longitudinal resistance. Under a strong magnetic field, the longitudinal resistance vanishes, whereas the Hall resistance remains at the quantized value. The realization of the QAH effect provides a foundation for many other novel quantum phenomena predicted in TIs, and opens a route to practical applications of quantum Hall physics in low-power-consumption electronics.
基金Majeed Ur Rehman acknowledges the support from the Chinese Academy of Sciences(CAS)and TWAS for his Ph.D.studies at the University of Science and Technology,China in the category of 2016 CAS-TWAS President’s Fellowship Awardee(Grant No.2016-156)
文摘The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number Cs for energy-bands of trilayer graphene having the essence of intrinsic spin-orbit coupling is analytically calculated. We find that for each valley and spin, Cs is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states, consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin-orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin-orbit （RSO） interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin-orbit coupling, while the other two layers have zero intrinsic spin-orbit coupling. Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.
基金Project supported by the National Basic Research Program of China(Grant Nos.2011CB922100,2011CBA00205,and 2013CB921804)the General Research Fund(GRF)of the Research Grants Council(RGC)of Hong Kong,China(Grant Nos.HKU7058/11P and HKU7045/13P)+6 种基金the Collaborative Research Fund(CRF)of the Research Grants Council(RGC)of Hong Kong,China(Grant No.HKU-8/11G)the University Research Committee(URC)Fund of the Hong Kong University(HKU),Chinathe National Natural Science Foundation of China(Grant Nos.11074111,11023002,and 11004065)the Priority Academic Program Development of Jiangsu Higher Education Institutions,Chinathe Program for New Century Excellent Talents in University of Ministry of Education of Chinathe Program for Changjiang Scholars and Innovative Research Team in University,Chinathe Fundamental Research Funds for the Central Universities of Ministry of Education of China
文摘We analyze the reading and initialization of a topological qubit encoded by Majorana fermions in one-dimensional semiconducting nanowires, weakly coupled to a single level quantum dot （QD）. It is shown that when the Majorana fermions are fused by tuning gate voltage, the topological qubit can be read out directly through the occupation of the QD in an energy window. The initialization of the qubit can also be realized via adjusting the gate voltage on the QD, with the total fermion parity conserved. As a result, both reading and initialization processes can be achieved in an all-electrical way.
文摘In this work, we discuss the topological transformation of quantum dynamics by showing the wave dynamics of a quantum particle on different types of topological structures in various dimensions from the fundamental polygons of the corresponding universal covering spaces. This is not the view from different perspectives of an observer who simply uses different coordinate systems to describe the same physical phenomenon but rather possible geometric and topological structures that quantum particles are endowed with when they are identified with differentiable manifolds that are embedded or immersed in Euclidean spaces of higher dimension. We present our discussions in the form of Bohr model in one, two and three dimensions using linear wave equations. In one dimension, the fundamental polygon is an interval and the universal covering space is the straight line and in this case the standing wave on a finite string is transformed into the standing wave on a circle which can be applied into the Bohr model of the hydrogen atom. In two dimensions, the fundamental polygon is a square and the universal covering space is the plane and in this case, the standing wave on the square is transformed into the standing wave on different surfaces that can be formed by gluing opposite sides of the square, which include a 2-sphere, a 2-torus, a Klein bottle and a projective plane. In three dimensions, the fundamental polygon is a cube and the universal covering space is the three-dimensional Euclidean space. It is shown that a 3-torus and the manifold K?× S1?defined as the product of a Klein bottle and a circle can be constructed by gluing opposite faces of a cube. Therefore, in three-dimensions, the standing wave on a cube is transformed into the standing wave on a 3-torus or on the manifold K?× S1. We also suggest that the mathematical degeneracy may play an important role in quantum dynamics and be associated with the concept of wavefunction collapse in quantum mechanics.
