Construction of Exact Invariants for Time Dependent Classical Dynamical Systems

In the present work, we survey various methodsused for the construction of exact invariants fordynamical systems involving an explicit time dependence.More stress is placed on two-dimensional (2D) than one-dimensional (1D) systems. While bothharmonic and anharmonic time-dependent (TD) systems arediscussed in the 1D case, the construction of invariantsis carried out for several interesting central and noncentral systems in 2D. The method ofcomplexification of two space dimensions is described indetail. The TD coupled oscillator problem, which in analternative form suggests the generalization of Ermakov systems, is analyzed in greater detail. Theavailable methods in the 2D case provide only the firstinvariant, and that for a few TD systems. These methodsas such are still inadequate as far as the construction of the second invariant is concerned. The roleand scope of some of the derived invariants in thecontext of various physical problems are highlighted.The possibility of extension of some of these methods to 3D TD systems is also discussed.     

四维相空间中非中心势动力学系统的Poisson 结构和Casimir 函数

将非中心势动力学系统的运动微分方程写成Ermakov形式，得到Ermakov不变量. 运用Hamilton理论，把Ermakov不变量当作Hamiltonian 函数，在四维相空间中建立了非中心势动力学系统的Poisson 结构。结果表明：此Poisson 结构是一退化的结构，而系统具有四个不变量，即Hamiltonian 函数，Ermakov不变量及两个Casimir函数。     

Quantum and classical spin clusters: disappearance of quantum numbers and Hamiltonian chaos

We present a direct link between manifestations of classical Hamiltonian chaos and quantum nonintegrability effects as they occur in quantum invariants. In integrable classical Hamiltonian systems, analytic invariants (integrals of the motion) can be constructed numerically by means of time averages of dynamical variables over phase-space trajectories, whereas in near-integrable models such time averages yield nonanalytic invariants with qualitatively different properties. Translated into quantum mechanics, the invariants obtained from time averages of dynamical variables in energy eigenstates provide a topographical map of the plane of quantized actions (quantum numbers) with properties which again depend sensitively on whether or not the classical integrability condition is satisfied. The most conspicuous indicator of quantum chaos is the disappearance of quantum numbers, a phenomenon directly related to the breakdown of invariant tori in the classical phase flow. All results are for a system consisting of two exchange-coupled spins with biaxial exchange and single-site anisotropy, a system with a nontrivial integrability condition.     

Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Disturbed Nonholonomic Systems

For a nonholonomic mechanics system with the action of small disturbance, the Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type are studied under general infinitesimal transformations of groups in which the generalized coordinates and time are variable. On the basis of the invariance of disturbed nonholonomic dynamical equations under general infinitesimal transformations, the determining equations, the constrained restriction equations and the additional restriction equations of Lie symmetries of the system are constructed, which only depend on the variables t, qs and q^.s. Based on the definition of higher-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for a nonholonomic system with the action of small disturbance is investigated, and the Lie symmetrical adiabatic invariants, the weakly Lie symmetrical adiabatic invariants and the strongly Lie symmetrical adiabatic invariants of generalized Hojman type of disturbed nonholonomic systems are obtained. An example is given to illustrate applications of the results.     

相空间中离散力学系统对称性的摄动与Hojman型绝热不变量

研究相空间中离散力学系统对称性的摄动与绝热不变量.列出相空间中未受扰离散力学系统的特殊Lie对称性导致的Hojman型精确不变量.基于相空间中力学系统的高阶绝热不变量的定义，研究在小扰动作用下系统Lie对称性的摄动，得到了相空间中离散力学系统的一类新的绝热不变量——Hojman型绝热不变量.举例说明结果的应用. 关键词： 相空间 Lie对称性 摄动 绝热不变量     

约束哈密顿系统在相空间中的精确不变量与绝热不变量

研究小干扰力作用下约束哈密顿系统对称性的摄动问题.建立了非保守约束哈密顿系统的正则方程,在增广相空间中研究了系统的对称性与精确不变量.基于力学系统的高阶绝热不变量的概念,给出了系统的各阶绝热不变量的形式及存在条件,并建立了绝热不变量与对称变换之间的对应关系 关键词： 约束哈密顿系统 对称性 摄动 不变量     

同步动态随机存储器辐射效应测试系统研制

在分析同步动态随机存储器(SDRAM)辐射效应主要失效现象的基础上,研制了具备了读写功能测试、刷新周期测试及功耗电流测试三种功能的SDRAM辐射效应在线测试系统,并开展了SDRAM的总剂量效应实验研究。结果表明,总剂量效应会导致SDRAM器件的数据保持时间不断减小,功耗电流不断增大以及读写功能失效。实验样品MT48LC8M32B2的功能失效主要由外围控制电路造成,而非存储单元翻转。数据保持时间虽然随着辐照剂量的累积不断减小,但不是造成该器件功能失效的直接原因。     

Kinetic Relaxation Models for Energy Transport

Kinetic equations with relaxation collision kernels are considered under the basic assumption of two collision invariants, namely mass and energy. The collision kernels are of BGK-type with a general local Gibbs state, which may be quite different from the Gaussian. By the use of the diffusive length/time scales, energy transport systems consisting of two parabolic equations with the position density and the energy density as unknowns are derived on a formal level. The H theorem for the kinetic model is presented, and the entropy for the energy transport systems, which is inherited from the kinetic model, is derived. The energy transport systems for specific examples of the global Gibbs state, such as a power law with negative exponent, a cut-off power law with positive exponent, the Maxwellian, Bose–Einstein, and Fermi–Dirac distributions, arepresented. MSC classification (2000): Primary: 82C40, 35B40; Secondary: 35K55, 45K05, 82D05, 85A05x     

Time dependent Thomas Fermi approach to atomic collisions II

Numerical solutions of the time dependent Thomas Fermi (TDTF) equations for central and noncentral proton-atom collisions are presented in the energy range between 27.5 and 900 keV. Different approximations to the TDTF equations are compared. A two step scheme is proposed for the reduction of the fluid dynamical time dependent Hartree Fock (TDHF) equations to an effective single particle problem.     

Perturbation to Lie Symmetry and Adiabatic Invariants for General Holonomic Mechanical Systems

Based on the concept of adiabatic invariant, the perturbation to the Lie symmetry and adiabatic invariants for general holonomic mechanical systems are studied. The exact invariants induced directly from the Lie symmetry of the system without perturbation are given. The perturbation to the Lie symmetry is discussed and the adiabatic invariants that have the different form from that in [Act. Phys. Sin. 55 (2006) 3236 (in Chinese)] of the perturbed system, are obtained.     

Complex energy plane and topological invariant in non-Hermitian systems

Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics. We propose a generalized local–global correspondence between the pseudo-boundary states in the complex energy plane and topological invariants of quantum states. We find that the patterns of the pseudo-boundary states in the complex energy plane mapped to the Brillouin zone are topological invariants against the parameter deformation. We demonstrate this approach by the non-Hermitian Chern insulator model. We give the consistent topological phases obtained from the Chern number and vorticity. We also find some novel topological invariants embedded in the topological phases of the Chern insulator model, which enrich the phase diagram of the non-Hermitian Chern insulators model beyond that predicted by the Chern number and vorticity. We also propose a generalized vorticity and its flipping index to understand physics behind this novel local–global correspondence and discuss the relationships between the local–global correspondence and the Chern number as well as the transformation between the Brillouin zone and the complex energy plane. These novel approaches provide insights to how topological invariants may be obtained from local information as well as the global property of quantum states, which is expected to be applicable in more generic non-Hermitian systems.     

Perturbation to Lie Symmetry and Adiabatic Invariants for General Holonomic Mechanical Systems

Based on the concept of adiabatic invariant, the perturbation to the Lie symmetry and adiabatic invariants for general holonomic mechanical systems are studied. The exact invariants induced directly from the Lie symmetry of the system without perturbation are given. The perturbation to the Lie symmetry is discussed and the adiabatic invariants that have the different form from that in [Act. Phys. Sin. 55 (2006) 3236 (in Chinese)] of the perturbed system, are obtained.     

Local Unitary Invariants for Multipartite Quantum Systems

We present an approach of constructing invariants under local unitary transformations for multipartite quantum systems. The invariants constructed in this way can be complement to that in [Science 340 (2013) 1205-1208]. Detailed examples are given to compute such invariant in detail. It is shown that these invariants can be used to detect the local unitary equivalence of degenerated quantum states.     

Model of pulsed electric discharge expansion in dense gas, taking into account electron and radiative thermal conductivities. V. Invariants of the set of equations describing the pulsed discharge

Similarity exponents of physical quantities of pulsed electric discharges in gases (at atmospheric pressure and above) and their dimensional invariants with respect to the linear coordinate and time transformation x?? _i = sx _i , t?? = st (s is the compression/stretching coefficient) are determined. Their dimensionless invariants are found from the invariance of the dimensionless continuity, motion, and energy balance equations with respect to the linear coordinate and time transformation. The values of the dimensionless invariants are determined from the condition of the uniform distribution of the plasma pressure in the discharge channel. Using these invariants, it became possible to reduce partial differential equations to ordinary differential equations solutions to which are used to determine the time dependences of the discharge channel radius and the time dependences of the plasma density and temperature (on the discharge channel axis) for the initial discharge stage.     

Rapid construction of solid-state magnetic resonance powder spectra from frequencies and amplitudes as applied to ESEEM

In many Fourier-transform spectroscopies, such as pulse magnetic resonance (NMR, EPR), time-domain signals are acquired. Parameters are extracted from these signals by fitting numerical simulations to the experimental data. At present, simulations are often performed in frequency domain (FD). These computations generate a list of frequencies and amplitudes associated with the complex exponential components evolving during one or several variable time intervals. In order to compare simulations with experiments, this peak list is converted to a finite-length time-domain (TD) signal. This can be achieved either by directly evoluting the exponentials in time (direct method) or by rounding their frequencies and binning their amplitudes into a frequency-domain array (histogram method). The first approach is equivalent to a brute-force TD simulation and is slow for a large number of peaks. The second approach is a fast, but very crude approximation and is usually applied without considering in detail the errors involved. A third method introduced and illustrated here is based on the convolution and deconvolution of a short finite impulse response filter kernel. This convolution approach is much faster than the direct method and by orders of magnitude more accurate than the histogram method. For both TD and FD signals a detailed analysis of the errors and of the associated computational costs is presented. The convolution approach is applicable to any simulation problem where TD signals consist of a large number of complex exponentials. In particular, it is the method of choice for simulating 1D and 2D electron spin echo envelope modulation (ESEEM) spectra of disordered systems.     

Suppressing the hot carrier injection degradation rate in total ionizing dose effect hardened nMOSFETs

Annular gate nMOSFETs are frequently used in spaceborne integrated circuits due to their intrinsic good capability of resisting total ionizing dose (TID) effect. However, their capability of resisting the hot carrier effect (HCE) has also been proven to be very weak. In this paper, the reason why the annular gate nMOSFETs have good TID but bad HCE resistance is discussed in detail, and an improved design to locate the source contacts only along one side of the annular gate is used to weaken the HCE degradation. The good TID and HCE hardened capability of the design are verified by the experiments for I/O and core nMOSFETs in a 0.18 μm bulk CMOS technology. In addition, the shortcoming of this design is also discussed and the TID and the HCE characteristics of the replacers (the annular source nMOSFETs) are also studied to provide a possible alternative for the designers.     

Topological Boundary Invariants for Floquet Systems and Quantum Walks

A Floquet systems is a periodically driven quantum system. It can be described by a Floquet operator. If this unitary operator has a gap in the spectrum, then one can define associated topological bulk invariants which can either only depend on the bands of the Floquet operator or also on the time as a variable. It is shown how a K-theoretic result combined with the bulk-boundary correspondence leads to edge invariants for the half-space Floquet operators. These results also apply to topological quantum walks.     

变质量单面完整约束系统Lie对称性的摄动与广义Hojman型绝热不变量

研究变质量单面完整约束系统Lie对称性的摄动与广义Hojman型绝热不变量.首先通过一般无限小变换下的Lie对称性得到广义Hojman型的守恒量；然后基于力学系统高阶绝热不变量的定义，研究小扰动作用下系统Lie对称性的摄动，得到系统广义Hojman型绝热不变量；最后举例说明结果的应用. 关键词： 变质量 单面完整约束 对称性 摄动 绝热不变量     

事件空间中完整系统的Lie对称性与绝热不变量

研究事件空间中完整力学系统Lie对称性的摄动与绝热不变量.基于力学系统的高阶绝热不变量的概念，研究在小扰动作用下系统Lie对称性的摄动，得到了事件空间中完整力学系统的一类Hojman形式的高阶绝热不变量，给出了绝热不变量存在的条件及形式.并举例说明结果的应用. 关键词： 事件空间 对称性 摄动 绝热不变量