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
The adaptive H_(∞) finite-time boundedness control problem is studied for a set of nonlinear singular Hamiltonian system(NSHS)in this article.Under an appropriate adaptive state feedback,the NSHS can be equivalently ...The adaptive H_(∞) finite-time boundedness control problem is studied for a set of nonlinear singular Hamiltonian system(NSHS)in this article.Under an appropriate adaptive state feedback,the NSHS can be equivalently transformed into a differential-algebraic system.Next,it is proved that the state feedback can be used as an adaptive H_(∞) finite-time boundedness controller of NSHS.Finally,the effectiveness of the controller designed is verified by an illustrative example of a nonlinear singular circuit system.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
For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy princi...For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy principal value is presented by using the spectral symmetry and new orthogonal relationship of the operators. Moreover, the above result is extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations.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 National Nature Science Foundation of China (61877028, 61773015).
文摘The adaptive H_(∞) finite-time boundedness control problem is studied for a set of nonlinear singular Hamiltonian system(NSHS)in this article.Under an appropriate adaptive state feedback,the NSHS can be equivalently transformed into a differential-algebraic system.Next,it is proved that the state feedback can be used as an adaptive H_(∞) finite-time boundedness controller of NSHS.Finally,the effectiveness of the controller designed is verified by an illustrative example of a nonlinear singular circuit system.
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.
基金Supported by the National Natural Science Foundation of China under Grant No. 10962004the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20070126002+1 种基金the Natural Science Foundation of Inner Mongolia under Grant No. 20080404MS0104the Research Foundation for Talented Scholars of Inner Mongolia University under Grant No. 207066
文摘For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy principal value is presented by using the spectral symmetry and new orthogonal relationship of the operators. Moreover, the above result is extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations.
