谐振子的辛欧拉分析方法

针对理想简谐振子力学模型,研究了其守恒律,并利用辛欧拉格式分析简谐振子振动过程.首先给出了谐振子系统的平方守恒律、周期守恒律和相差守恒律.构造了谐振子的普通欧拉格式和辛欧拉格式,研究了两种格式下三种守恒律各自的保持情况.模拟结果显示:辛欧拉格式能够精确保持时域守恒律(平方守恒律),但无法保持频域守恒律(周期守恒律和相差守恒律).如要克服辛欧拉格式的不足,需按邢誉峰教授提出的方法进行校正.     

A family of smooth controllers for swinging up a pendulum

The paper presents a new family of controllers for swinging up a pendulum. The swinging up of the pendulum is derived from physical arguments based on two ideas: shaping the Hamiltonian for a system without damping; and providing damping or energy pumping in relevant regions of the state space. A family of simple smooth controllers without switches with nice properties is obtained. The main result is that all solutions that do not start at a zero Lebesgue measure set converge to the upright position for a wide range of the parameters in the control law. Thus, the swing-up and the stabilization problems are simultaneously solved with a single, smooth law. The properties of the solution can be modified by the parameters in the control law. Control signal saturation can also be taken into account using the Hamiltonian approach.     

Quantum mechanics at the core of multi-scale simulations

Quantum mechancial forces at the core of multi-scale simulations, require a one-electron Hamiltonian approach whose solution provide electronic energies, forces, and properties for > 1,000 atoms fast enough that it can drive large scale molecular dynamics. Such a transfer-Hamiltonian is hoped to be as predictive as accurate, ab initio quantum chemistry for such systems. To design the Hamiltonian requires that, we investigate rigorous one-particle theories including density functional theory (DFT) and the recently proposed, correlated orbital potential (COP) approach that has been developed solely from wavefunction considerations. The latter insists upon exact, principal ionization potentials and electron affinities for a system, while DFT insists upon the exact density and the HOMO ionization. These two complementary approaches help identify the essential quantities that an exact one-particle theory of electronic structure requires. The intent, then, is to incorporate these into a simple approximation that can provide the accuracy required but at a speed four orders of magnitude faster than today’s DFT. The theory is presented and its neglect of diatomic differential overlap (NDDO) realization is illustrated for select systems.     

Treating the Independent Set Problem by 2D Ising Interactions with Adiabatic Quantum Computing

We construct a nearest-neighbor interaction whose ground states encode the solutions to the NP-complete problem independent set for cubic planar graphs. The important difference to previously used Hamiltonians in adiabatic quantum computing is that our Hamiltonian is spatially local. Due to its special structure our Hamiltonian can be easily simulated by Ising interactions between adjacent particles on a 2D rectangular lattice. We describe the required pulse sequences. Our methods could help to implement adiabatic quantum computing by physically reasonable Hamiltonians like short-range interactions. Therefore, this universal resource Hamiltonian can be used for different graphs by applying suitable control operations. This is in contrast to a previous proposal where the Hamiltonians have to be wired in hardware for each graph. PACS: 03.67.Lx     

奇异系统的量子Poincaré-Cartan积分不变量

为了研究奇异Lagrange量系统(奇异系统)的对称性问题,从有限自由度系统相空间Green函数生成泛函出发,导出了奇异系统量子情形的Poincare-Cartan(PC)积分不变量,其中不包含系统基态符号|0>．讨论了该不变量与Hamilton-Jacobi方程的关系,指出由PC积分不变量可导致量子水平的Hamilton-Jacobi方程．     

Periodic Anderson model for the description of noncollinear magnetic structure in low-dimensional 3d-systems

Distribution of magnetic moments in the low-dimensional metallic structures has been studied theoretically on the basis of periodic Anderson model. Calculation of noncollinear magnetic order was performed in the Hartree-Fock approximation using tight binding real space recursion method. Iteration process includes self-consistent determination of population numbers for the electrons with different directions of the magnetic moments at given atom relatively to the fixed axis. Energies of all states corresponding to the different directions of magnetic moments at the atom under consideration have been calculated, and the state with minimal energy being accepted for the next step.

Analytical transformations based on the generalised “zeros and poles method” were performed for the Green function that allows to avoid some time-consuming numerical procedures. It gives the possibility to develop efficient algorithm for the calculation of noncollinear magnetic structure of complex space nonhomogeneous systems.

Calculations performed for the parameters corresponding to Fe and Cr show the qualitatively different dependencies of the magnetic moment magnitude and the energies of d-electrons on the angles, which define the direction of magnetic moments.     

Model Calculation of Distance-Dependent Electron–Phonon Coupling Parameters Derived from One- and Two-Body Interactions for a Dimer

We evaluate all the electron–phonon coupling terms derived from one and two-body electronic interactions, in both the adiabatic and the extreme nonadiabatic limit, for a dimer with a nondegenerate orbital built from atomic wave functions of Gaussian shape. Different forms of the Hamiltonian contributions result in the two limits.     

基于激发态的哈密顿量等级系统

超对称性量子力学中的超势可以利用激发态来生成，得到广义超对称形成。因此，能够利用广义超对称形成，可构成出与已知哈密顿量等能谱的哈密顿量等级系统，再以线性谱振子为例说明.     

A theoretical analysis of zero-field splitting parameters of Mn doped dicadmium diammonium sulfate Cd2(NH4)2(SO4)3 single crystal

The superposition model (SPM) and crystallographic data are utilized to determine the zero-field splitting (ZFS) parameters (ZFSPs) for Mn²⁺ ions in Cd₂(NH₄)₂(SO₄)₃ single crystal, assuming that the Mn²⁺ ions locate at either Cd²⁺ or NH⁴⁺ site. The SPM results has been verified by the fourth-order perturbation formulae analysis. Experimental suggestions about Mn²⁺ ions substituting at Cd²⁺ sites have been confirmed theoretically for the first time.     

并联混合有源滤波器哈密顿系统建模及无源控制

并联混合有源滤波器(SHAPF)的控制策略是决定其稳定性和谐波治理效果的关键因素之一,利用SHAPF自身的无源性设计控制器可以取得比常规控制器更好的控制效果.首先建立了SHAPF端口受控哈密顿系统模型,然后基于互联和阻尼配置无源控制方法,提出了一种新的SHAPF非线性控制策略,从理论上保证了闭环系统的渐进稳定.最后仿真实验证明了该控制策略能够有效消除电网中的谐波电流,与传统线性二次型调节器(LQR)相比,该控制策略具有更好的稳态补偿效果和对负载变化的干扰抑制能力.