We investigate the quantum dynamics of the 1D spinless Fermi-Hubbard model with a linear-tilted potential.Surprisingly in a strong resonance regime,we show that the model can be described by the kinetically constraine...We investigate the quantum dynamics of the 1D spinless Fermi-Hubbard model with a linear-tilted potential.Surprisingly in a strong resonance regime,we show that the model can be described by the kinetically constrained effective Hamiltonian,and it can be spontaneously divided into two commuting parts dubbed Hamiltonian dimerization,which are composed of two distinct sets of constrained nearest-neighbor hopping terms:one set acting exclusively on odd bonds and the other on even bonds.Specifically it is shown that each part can be independently mapped onto the well-known PXP model;therefore the dimerized Hamiltonian is equivalent to a two-fold PXP model.As a consequence,we numerically demonstrate this system can host the so-called quantum many-body scars,which present dynamical revivals and ergodicity-breaking behaviors.However,in sharp contrast with traditional quantum many-body scars,here the scarring states in our model driven by different parts of the Hamiltonian will revive in different periods,and those of double parts can display a biperiodic revival pattern,both originating from the Hamiltonian dimerization.Besides,the condition of off-resonance is also discussed,and we show the crossover from quantum many-body scar to ergodicity breaking is diagnosed via level statistics.Our model provides a platform for understanding the interplay of Hilbert space fragmentation and the constrained quantum systems.展开更多
In this paper,the problem of brake orbits with minimal period estimates are considered for the first-order Hamiltonian systems with anisotropic growth,i.e.,the Hamiltonian functions may have super-quadratic,sub-quadra...In this paper,the problem of brake orbits with minimal period estimates are considered for the first-order Hamiltonian systems with anisotropic growth,i.e.,the Hamiltonian functions may have super-quadratic,sub-quadratic and quadratic behaviors simultaneously in different variable components.展开更多
This paper is concerned with the existence of nontrivial homoclinic solutions for a class of second order Hamiltonian systems with external forc-ing perturbations q+Aq+Vq(t,q)=f(t),where q=(q1,q2,..qN)∈R^(N),A is an ...This paper is concerned with the existence of nontrivial homoclinic solutions for a class of second order Hamiltonian systems with external forc-ing perturbations q+Aq+Vq(t,q)=f(t),where q=(q1,q2,..qN)∈R^(N),A is an antisymmetric constant N×N matrix,V(t,q)=-K(t,q)+W(t,q)with K,W ∈C^(1)(R,R^(N))and satisfying b1|q|^(2)≤K(t,q)≤b_(2)|q|^(2)for some positive constants b_(2)≥b_(1)>0 and external forcing term f∈C(R,R^(N))being small enough.Under some new weak superquadratic conditions for W,by using the mountain pass theorem,we obtain the existence of at least one nontrivial homoclinic solution.展开更多
A Hamiltonian mean-field model with long-range four-body interactions is proposed.The model describes a long-range mean-field system in which N unit-mass particles move on a unit circle.Each particleθi interacts with...A Hamiltonian mean-field model with long-range four-body interactions is proposed.The model describes a long-range mean-field system in which N unit-mass particles move on a unit circle.Each particleθi interacts with any three other particles through an infinite-range cosine potential with an attractive interaction(ε>0).By applying a method that remaps the average phase of global particle pairs onto a new unit circle,and using the saddle-point technique,the partition function is solved analytically after introducing four-body interactions,yielding expressions for the free energy f and the energy per particle U.These results were further validated through numerical simulations.The results show that the system undergoes a second-order phase transition at the critical energy Uc.Specifically,the critical energy corresponds to U_(c)=0.32 when the coupling constantε=5,and U_(c)=0.63 whenε=10.Finally,we calculated the system’s largest Lyapunov exponentλand kinetic energy fluctuationsΣthrough numerical simulations.It is found that the peak of the largest Lyapunov exponentλoccurs slightly below the critical energy Uc,which is consistent with the point of maximum kinetic energy fluctuationsΣ.And there is a scaling law ofΣ/N^(1/2)∝λbetween them.展开更多
Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characteri...Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characterization of G for which L^(n)(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph.展开更多
A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions o...A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.展开更多
A graph G possesses Hamiltonian s-properties when G is Hamilton-connected if s=1,Hamiltonian if s=0,and traceable if s=-1.Let S_A(G)=λ_n(G)-λ_1(G)and S_L(G)=μ_n(G)-μ_2(G)be the spread and the Laplacian spread of G...A graph G possesses Hamiltonian s-properties when G is Hamilton-connected if s=1,Hamiltonian if s=0,and traceable if s=-1.Let S_A(G)=λ_n(G)-λ_1(G)and S_L(G)=μ_n(G)-μ_2(G)be the spread and the Laplacian spread of G,respectively,whereλ_n(G)andλ_1(G)are the largest and smallest eigenvalues of G,andμ_n(G)andμ_2(G)are the largest and second smallest Laplacian eigenvalues of G,respectively.In this paper,we shall present two sufficient conditions involving S_A(G)and S_L(G)for a k-connected graph to possess Hamiltonian s-properties,respectively.We also derive a sufficient condition on the Laplacian eigenratio μ2(G)/μ(G) for a k-connected graph to possess Hamiltonian s-properties.展开更多
While density functional theory(DFT)serves as a prevalent computational approach in electronic structure calculations,its computational demands and scalability limitations persist.Recently,leveraging neural networks t...While density functional theory(DFT)serves as a prevalent computational approach in electronic structure calculations,its computational demands and scalability limitations persist.Recently,leveraging neural networks to parameterize the Kohn-Sham DFT Hamiltonian has emerged as a promising avenue for accelerating electronic structure computations.Despite advancements,challenges such as the necessity for computing extensive DFT training data to explore each new system and the complexity of establishing accurate machine learning models for multi-elemental materials still exist.Addressing these hurdles,this study introduces a universal electronic Hamiltonian model trained on Hamiltonian matrices obtained from first-principles DFT calculations of nearly all crystal structures on the Materials Project.We demonstrate its generality in predicting electronic structures across the whole periodic table,including complex multi-elemental systems,solid-state electrolytes,Moir´e twisted bilayer heterostructure,and metal-organic frameworks.Moreover,we utilize the universal model to conduct high-throughput calculations of electronic structures for crystals in GNoME datasets,identifying 3940 crystals with direct band gaps and 5109 crystals with flat bands.By offering a reliable efficient framework for computing electronic properties,this universal Hamiltonian model lays the groundwork for advancements in diverse fields,such as easily providing a huge data set of electronic structures and also making the materials design across the whole periodic table possible.展开更多
[App1.Anal.Discrete Math.,2017,11(1):81-107] defined the A_α-matrix of a graph G as A_α(G)=αD(G)+(1-α)A(G),where α∈[0,1],D(G) and A(G) are the diagonal matrix of degrees and the adjacency matrix of G,respectivel...[App1.Anal.Discrete Math.,2017,11(1):81-107] defined the A_α-matrix of a graph G as A_α(G)=αD(G)+(1-α)A(G),where α∈[0,1],D(G) and A(G) are the diagonal matrix of degrees and the adjacency matrix of G,respectively.The largest eigenvalue of A_α(G) is called the A_α-spectral radius of G,denoted by ρ_α(G).In this paper,we give an upper bound on ρ_α(G) of a Hamiltonian graph G with m edges for α∈[1/2,1),and completely characterize the corresponding extremal graph in the case when m is odd.In order to complete the proof of the main result,we give a sharp upper bound on the ρ_α(G) of a connected graph G in terms of its degree sequence.展开更多
We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and the...We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.展开更多
在计算机视觉领域,由镜头切换、目标动力学突变、低帧率视频等引起的突变运动存在极大的不确定性,使得突变运动跟踪成为该领域的挑战性课题.以贝叶斯滤波框架为基础,提出一种基于有序超松弛Hamiltonian马氏链蒙特卡罗方法的突变运动跟...在计算机视觉领域,由镜头切换、目标动力学突变、低帧率视频等引起的突变运动存在极大的不确定性,使得突变运动跟踪成为该领域的挑战性课题.以贝叶斯滤波框架为基础,提出一种基于有序超松弛Hamiltonian马氏链蒙特卡罗方法的突变运动跟踪算法.该算法将Hamiltonian动力学融入MCMC(Markov chain Monte Carlo)算法,目标状态被扩张为原始目标状态变量与一个动量项的组合.在提议阶段,为抑制由Gibbs采样带来的随机游动行为,提出采用有序超松弛迭代方法来抽取目标动量项.同时,提出自适应步长的Hamiltonian动力学实现方法,在跟踪过程中自适应地调整步长,以减少模拟误差.提出的跟踪算法可以避免传统的基于随机游动的MCMC跟踪算法所存在的局部最优问题,提高了跟踪的准确性而不需要额外的计算时间.实验结果表明,该算法在处理多种类型的突变运动时表现出出色的处理能力.展开更多
基金supported by the National Key R&D Program of China(Grant No.2023YFA1406002)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301200)。
文摘We investigate the quantum dynamics of the 1D spinless Fermi-Hubbard model with a linear-tilted potential.Surprisingly in a strong resonance regime,we show that the model can be described by the kinetically constrained effective Hamiltonian,and it can be spontaneously divided into two commuting parts dubbed Hamiltonian dimerization,which are composed of two distinct sets of constrained nearest-neighbor hopping terms:one set acting exclusively on odd bonds and the other on even bonds.Specifically it is shown that each part can be independently mapped onto the well-known PXP model;therefore the dimerized Hamiltonian is equivalent to a two-fold PXP model.As a consequence,we numerically demonstrate this system can host the so-called quantum many-body scars,which present dynamical revivals and ergodicity-breaking behaviors.However,in sharp contrast with traditional quantum many-body scars,here the scarring states in our model driven by different parts of the Hamiltonian will revive in different periods,and those of double parts can display a biperiodic revival pattern,both originating from the Hamiltonian dimerization.Besides,the condition of off-resonance is also discussed,and we show the crossover from quantum many-body scar to ergodicity breaking is diagnosed via level statistics.Our model provides a platform for understanding the interplay of Hilbert space fragmentation and the constrained quantum systems.
基金supported by the NSFC(12301138)the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(2021L377)+1 种基金the Doctoral Scientific Research Foundation of Shanxi Datong University(2018-B-15)The second author’s work was supported by the NSFC(12171108).
文摘In this paper,the problem of brake orbits with minimal period estimates are considered for the first-order Hamiltonian systems with anisotropic growth,i.e.,the Hamiltonian functions may have super-quadratic,sub-quadratic and quadratic behaviors simultaneously in different variable components.
基金supported by the National Natural Science Foundation of China(Grant No.12171253).
文摘This paper is concerned with the existence of nontrivial homoclinic solutions for a class of second order Hamiltonian systems with external forc-ing perturbations q+Aq+Vq(t,q)=f(t),where q=(q1,q2,..qN)∈R^(N),A is an antisymmetric constant N×N matrix,V(t,q)=-K(t,q)+W(t,q)with K,W ∈C^(1)(R,R^(N))and satisfying b1|q|^(2)≤K(t,q)≤b_(2)|q|^(2)for some positive constants b_(2)≥b_(1)>0 and external forcing term f∈C(R,R^(N))being small enough.Under some new weak superquadratic conditions for W,by using the mountain pass theorem,we obtain the existence of at least one nontrivial homoclinic solution.
基金supported by the National Natural Science Foundation of China(Grant No.11962002)the Innovation Project of the Guangxi Graduate Education(Grant Nos.YCBZ2021021 and YCSW2022070).
文摘A Hamiltonian mean-field model with long-range four-body interactions is proposed.The model describes a long-range mean-field system in which N unit-mass particles move on a unit circle.Each particleθi interacts with any three other particles through an infinite-range cosine potential with an attractive interaction(ε>0).By applying a method that remaps the average phase of global particle pairs onto a new unit circle,and using the saddle-point technique,the partition function is solved analytically after introducing four-body interactions,yielding expressions for the free energy f and the energy per particle U.These results were further validated through numerical simulations.The results show that the system undergoes a second-order phase transition at the critical energy Uc.Specifically,the critical energy corresponds to U_(c)=0.32 when the coupling constantε=5,and U_(c)=0.63 whenε=10.Finally,we calculated the system’s largest Lyapunov exponentλand kinetic energy fluctuationsΣthrough numerical simulations.It is found that the peak of the largest Lyapunov exponentλoccurs slightly below the critical energy Uc,which is consistent with the point of maximum kinetic energy fluctuationsΣ.And there is a scaling law ofΣ/N^(1/2)∝λbetween them.
基金Supported by the Natural Science Foundation of China(12131013,12371356)the special fund for Science and Technology Innovation Teams of Shanxi Province(202204051002015)the Fundamental Research Program of Shanxi Province(202303021221064).
文摘Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characterization of G for which L^(n)(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12261064 and 11861048)the Natural Science Foundation of Inner Mongolia,China (Grant Nos.2021MS01004 and 2022QN01008)the High-level Talents Scientific Research Start-up Foundation of Inner Mongolia University (Grant No.10000-21311201/165)。
文摘A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.
基金Supported by NSFC(Nos.12171089,12271235)NSF of Fujian Province(No.2021J02048)。
文摘A graph G possesses Hamiltonian s-properties when G is Hamilton-connected if s=1,Hamiltonian if s=0,and traceable if s=-1.Let S_A(G)=λ_n(G)-λ_1(G)and S_L(G)=μ_n(G)-μ_2(G)be the spread and the Laplacian spread of G,respectively,whereλ_n(G)andλ_1(G)are the largest and smallest eigenvalues of G,andμ_n(G)andμ_2(G)are the largest and second smallest Laplacian eigenvalues of G,respectively.In this paper,we shall present two sufficient conditions involving S_A(G)and S_L(G)for a k-connected graph to possess Hamiltonian s-properties,respectively.We also derive a sufficient condition on the Laplacian eigenratio μ2(G)/μ(G) for a k-connected graph to possess Hamiltonian s-properties.
基金supported the National Key R&D Program of China (Grant No.2022YFA1402901)the National Natural Science Foundation of China (Grant Nos.11825403,11991061,and 12188101)the Guangdong Major Project of the Basic and Applied Basic Research (Future Functional Materials Under Extreme Conditions) (Grant No.2021B0301030005)。
文摘While density functional theory(DFT)serves as a prevalent computational approach in electronic structure calculations,its computational demands and scalability limitations persist.Recently,leveraging neural networks to parameterize the Kohn-Sham DFT Hamiltonian has emerged as a promising avenue for accelerating electronic structure computations.Despite advancements,challenges such as the necessity for computing extensive DFT training data to explore each new system and the complexity of establishing accurate machine learning models for multi-elemental materials still exist.Addressing these hurdles,this study introduces a universal electronic Hamiltonian model trained on Hamiltonian matrices obtained from first-principles DFT calculations of nearly all crystal structures on the Materials Project.We demonstrate its generality in predicting electronic structures across the whole periodic table,including complex multi-elemental systems,solid-state electrolytes,Moir´e twisted bilayer heterostructure,and metal-organic frameworks.Moreover,we utilize the universal model to conduct high-throughput calculations of electronic structures for crystals in GNoME datasets,identifying 3940 crystals with direct band gaps and 5109 crystals with flat bands.By offering a reliable efficient framework for computing electronic properties,this universal Hamiltonian model lays the groundwork for advancements in diverse fields,such as easily providing a huge data set of electronic structures and also making the materials design across the whole periodic table possible.
文摘[App1.Anal.Discrete Math.,2017,11(1):81-107] defined the A_α-matrix of a graph G as A_α(G)=αD(G)+(1-α)A(G),where α∈[0,1],D(G) and A(G) are the diagonal matrix of degrees and the adjacency matrix of G,respectively.The largest eigenvalue of A_α(G) is called the A_α-spectral radius of G,denoted by ρ_α(G).In this paper,we give an upper bound on ρ_α(G) of a Hamiltonian graph G with m edges for α∈[1/2,1),and completely characterize the corresponding extremal graph in the case when m is odd.In order to complete the proof of the main result,we give a sharp upper bound on the ρ_α(G) of a connected graph G in terms of its degree sequence.
文摘We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.
文摘在计算机视觉领域,由镜头切换、目标动力学突变、低帧率视频等引起的突变运动存在极大的不确定性,使得突变运动跟踪成为该领域的挑战性课题.以贝叶斯滤波框架为基础,提出一种基于有序超松弛Hamiltonian马氏链蒙特卡罗方法的突变运动跟踪算法.该算法将Hamiltonian动力学融入MCMC(Markov chain Monte Carlo)算法,目标状态被扩张为原始目标状态变量与一个动量项的组合.在提议阶段,为抑制由Gibbs采样带来的随机游动行为,提出采用有序超松弛迭代方法来抽取目标动量项.同时,提出自适应步长的Hamiltonian动力学实现方法,在跟踪过程中自适应地调整步长,以减少模拟误差.提出的跟踪算法可以避免传统的基于随机游动的MCMC跟踪算法所存在的局部最优问题,提高了跟踪的准确性而不需要额外的计算时间.实验结果表明,该算法在处理多种类型的突变运动时表现出出色的处理能力.
