Energy Separation in Oscillatory Hamiltonian Systems without any Non-resonance Condition

We consider multiscale Hamiltonian systems in which harmonic oscillators with several high frequencies are coupled to a slow system. It is shown that the oscillatory energy is nearly preserved over long times ${\varepsilon^{-N}}$ for arbitrary N > 1, where ${\varepsilon^{-1}}$ is the size of the smallest high frequency. The result is uniform in the frequencies and does not require non-resonance conditions.     

Semianalytical method for treatment of the N-body problem with complex total energy within the hyperharmonics approach

We develop the variable phase approach to analyze all the solutions of the N-body hyperradial equations. As a first result of this analysis, we display here how the usual cutoff of the long-range potential matrix generates unphysical solutions. As an example of such solutions we present a set of unphysical three-neutron resonances. To overcome this peculiarity of the standard hyperharmonics approach we introduce a well-defined solution of the Jost-type and construct it at large hyperradius analytically.     

Quantum states far from the energy eigenstates of any local Hamiltonian

What quantum states are possible energy eigenstates of a many-body Hamiltonian? Suppose the Hamiltonian is nontrivial, i.e., not a multiple of the identity, and L local, in the sense of containing interaction terms involving at most L bodies, for some fixed L. We construct quantum states psi which are "far away" from all the eigenstates E of any nontrivial L-local Hamiltonian, in the sense that ||psi-E|| is greater than some constant lower bound, independent of the form of the Hamiltonian.     

Exact self-gravitating N-body motion in the CGHS model

In the asymptotically flat two-dimensional dilaton gravity, we present an N-body particle action which has a dilaton coupled mass term for the exact solubility. This gives nonperturbative exact solutions for the N-body self-gravitating system, so the infalling particles form a black hole and their trajectories are exactly described. In our two-dimensional case, the critical mass for the formation of black holes does not exist, so even a single particle forms a black hole. The infalling particles give additional time-like singularities in addition to the space-like black hole singularity. However, the latter singularities can be properly cloaked by the future horizons within some conditions.     

Integer quantum hall effect between any two points in the system

The Hall current flowing across an arbitrary curve connecting any two points selected in a high mobility, dissipation free, integer quantum Hall system shows quantised nature with respect to the potential difference between the two points. The Hall conductance can therefore be defined between any two points in the sample. For a given system, the behaviour of this Hall conductance depends on the potential difference between the two selected points only. The overall quantum Hall behaviour can be derived in a special case when the two points are selected at the Hall contacts.     

New relative equilibria of the N-body problem

We announce several theorems on the nature of new relative equilibria classes in the planar n-body problem of celestial mechanics. Their existence is suggested by the creation and annihilation of relative equilibria at degenerate relative equilibria classes. We announced several basic new results in [2], [4]. We refer to these papers for definitions left unspecified here.Research supported in part by NSF grant MPS-73-03735A04     

Completeness of Bethe type eigenfunctions for the 1D N-body system with δ-function interactions

By extending the original domain of definition for the wavefunctions to the whole space periodically so that the translation symmetry can be applied, a rigorous proof is given for the completeness of the “Bethe type” eigenfunctions in the 1D N-body systems with δ-function interactions proposed by Lieb and Liniger, and Yang.     

Embedding any desired number of coexisting attractors in memristive system

A simple variable-boostable system is selected as the structure for hosting an arbitrarily defined memristor for chaos producing. The derived three-dimensional (3-D) memristive chaotic system shows its distinct property of offset, amplitude and frequency control. Owing its merits any desired number of coexisting attractors are embedded by means of attractor doubling and self-reproducing based on function-oriented offset boosting. In this circumstance two classes of control gates are found:one determines the number of coexisting attractors resorting to the independent offset controller while the other is the initial condition selecting any one of them. Circuit simulation gives a consistent output with theoretically predicted embedded attractors.     

Two-dimensional potential energy function for internal rotation in 1,2-dihydroxybenzenes

We have obtained an analytical expression for the two-dimensional potential energy function for internal rotation in 1,2-dihydroxybenzenes, allowing us to use perturbation theory methods to calculate and interpret the torsional spectra of these compounds. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 1, pp. 133–136, January–February, 2006.     

Spin rotation and oscillation of high energy particles in storage ring

Phenomena of rotation and oscillations of particle spin are discussed for particles rotating in storage ring. The fact that these effects are described by spin-dependent part of zero-angle scattering amplitude allows to use them for the measurement of this amplitude at different energies of colliding particles. It is shown that effect magnitudes are large and they can be observed at the existing accelerators.     

Phase rotation scheme of laser-produced ions for reduction of the energy spread

In order to widely spread out particle beams utilized in cancer therapy, laser-produced ions are developed as the injection beam for an ion synchrotron dedicated for cancer therapy. Such a laser ion source is expected to contribute largely to the realization of compactness of the size and low cost of the cancer therapy accelerator. The energy spectrum of the laser-produced ions, however, has no peak, but their intensities decrease exponentially according to the increase of the energy. For the purpose of modifying such a situation, we have proposed a scheme to rotate the beam in the longitudinal phase space with the use of the RF electric field, which is phase-adjusted with the pulse laser. We aim for a reduction of the energy spread of ± 5% selected by an energy analyzer and slits to ±1% by such phase rotation. For this purpose, a quarter wavelength resonator with two gaps with the same resonant frequency as the source laser has already been fabricated, together with its RF power source. The above phase rotation system and its recent experimental realization are presented.     

CO-- He 碰撞系统态-态传能截面的研究

通过波恩近似理论对双原子激发态转动传能中量子干涉效应相关信息进行深入研究,利用各向异性相互作用势建立了传能截面的理论模型,得到了转动传能因碰撞能量的不同而产生的差异,传能截面随着初末量子数、散射角的变化关系。讨论了散射角和碰撞能量对传能截面的影响。     

Perturbations in the vibration-rotation-torsion energy levels of an ethane molecule exhibiting internal rotation splittings

Various examples of perturbations in the vibration-rotation-torsion energy levels of an ethane molecule exhibiting internal rotation splittings are discussed, both from the point of view of the point group D_3d, appropriate when internal rotation tunneling effects cannot be observed, and from the point of view of the group $\text{G}{}_{36}{}^2$, appropriate when internal rotation tunneling in ethane leads to observable splittings in the spectrum. It is found, for perturbations allowed in both D_3d and $\text{G}{}_{36}{}^2$, that each of the two torsional components of the perturbed D_3d vibration-rotation level can in principle interact with a “corresponding” torsional component in the perturbing vibration-rotation level. It is found for perturbations forbidden in D_3d but allowed in $\text{G}{}_{36}{}^2$, which all occur between D_3d vibrational levels of different g, u parity, that only one of the two torsional components of the perturbed D_3d vibration-rotation level can interact with a corresponding torsional component in the perturbing vibration-rotation level. Some of the perturbations examined give intensity to otherwise forbidden transitions in such a way that perturbation-induced transitions can be used in conjunction with normally allowed transitions to determine the sum of the internal rotation splittings for two rotational levels differing in K by three units.     

成像型任意反射面速度干涉仪的散斑抑制

成像型任意反射面速度干涉仪(VISAR)是激光驱动聚变实验中诊断冲击波速度的重要设备。由于采用了激光照明靶面的方式,所获得的速度条纹图中不可避免有激光散斑的干扰,严重影响动态条纹的质量。介绍了该系统的激光散斑形成原因和散斑对速度分析的影响,提出了一种频谱面滤波的方式去除高频散斑噪声的方法,并通过搭建散斑光路、合理设置滤波孔位置和大小,对该方法进行了验证。结果表明,该方法对影响条纹图的高频散斑噪声具有抑制作用,适合应用于成像型VISAR系统。     

成像型任意反射面速度干涉仪的散斑抑制

成像型任意反射面速度干涉仪（VISAR）是激光驱动聚变实验中诊断冲击波速度的重要设备。由于采用了激光照明靶面的方式,所获得的速度条纹图中不可避免有激光散斑的干扰,严重影响动态条纹的质量。介绍了该系统的激光散斑形成原因和散斑对速度分析的影响,提出了一种频谱面滤波的方式去除高频散斑噪声的方法,并通过搭建散斑光路、合理设置滤波孔位置和大小,对该方法进行了验证。结果表明,该方法对影响条纹图的高频散斑噪声具有抑制作用,适合应用于成像型VISAR系统。     

Chaotic versus nonchaotic stochastic dynamics in Monte Carlo simulations: a route for accurate energy differences in N-body systems

We present a method to efficiently evaluate small energy differences of two close N-body systems by employing stochastic processes having a stability versus chaos property. By using the same random noise, energy differences are computed from close trajectories without reweighting procedures. The approach is presented for quantum systems but can be applied to classical N-body systems as well. It is exemplified with diffusion Monte Carlo simulations for long chains of hydrogen atoms and molecules for which it is shown that the long-standing problem of computing energy derivatives is solved.     

Determination of the energy levels of total and internal rotation of arbitrary polyatomic molecules with a single internal rotation axis

An algorithm is developed for calculating the eigenvalues of the Hamiltonian operator in the case of asymmetric-asymmetric molecules with a common axis of internal rotation, taking into account the total and internal rotation of these molecules. The algorithm is based on the Ritz variational method. A program is written for reducing a symmetric band matrix to tridiagonal form with subsequent diagonalization of the resulting matrix.State Textile Academy, Ivanovo. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 81–88, October, 1995.     

在局域子空间中计算给定范围内的能量本征值

通过能量算符δ函数作用于完全随机格点波函数,构造了可用于直接计算给定范围[Emin,Emax]内能量本征值和本征函数的局域子空间.在非正交局域基下详细推导了交迭积分和哈密顿算符在分立位置表象中的表示,讨论了广义本征值问题的解法.以Morse势和Henon-Heiles势的多个能量范围为例检验了算法