垂直振动激发下颗粒物质的能量耗散

本文对垂直振动激发下的铜和玻璃珠两种密集颗粒样品,通过实时测量样品盒的加速度和振台对它的作用力,研究了样品的平均耗散功率.实验发现该耗散功率在给定振动强度下随振动频率的变化曲线是一个峰值在几十赫兹的宽峰结构,在给定频率下随强度的变化具有幂率规律,其幂值小于简谐受迫振动模型的幂值2.这些结果将有助于研究测定颗粒流体和气体的迁移系数,以及它们在不同运动模式下的能耗差异.     

均匀磁场中二维各向同性带电谐振子的守恒量与对称性研究

由牛顿第二定律得到二维各向同性带电谐振子在均匀磁场中运动的运动微分方程,通过对运动微分方程的直接积分得到系统的两个积分(守恒量).利用Legendre变换建立守恒量与Lagrange函数间的关系,从而求得系统的Lagrange函数,并讨论与守恒量相应的无限小变换的Noether对称性与Lie对称性,最后求得系统的运动学方程.     

Power Series Expansion of Propagator for Path Integral and Its Applications

In this paper we obtain a propagator of path integral for a harmonic oscillator and a driven harmonic oscillator by using the power series expansion. It is shown that our result for the harmonic oscillator is more exact than the previous one obtained with other approximation methods. By using the same method, we obtain a propagator of path integral for the driven harmonic oscillator, which does not have any exact expansion. The more exact propagators may improve the path integral results for these systems.     

Fractional extensions of the classical isotropic oscillator and the Kepler problem

The class of fractional Hamiltonian systems that generalize the classical problem of the two-dimensional (2D) isotropic harmonic oscillator and the Kepler problem is considered. It is shown that, in the 4D space of structural parameters, the 2D isotropic harmonic oscillator can be extended along a line in such a way that the orbits remain closed and oscillations remain isochronous. Likewise, the Kepler problem can be extended along a line in such a way that the orbits remain closed for all finite motions and the third Kepler law remains valid. These curves lie on the 2D surfaces where any dynamical system is characterized by the same rotation number for all finite motions.     

简谐速度噪声与简谐噪声环境中谐振子的动力学共振

通过求解简谐势场中的广义量子朗之万方程，得到平均能量的精确表达式.由于简谐速度噪声与简谐噪声功率谱的不同特点，两种内部噪声驱动的谐振子在简谐外力的作用下具有不同的共振特征.这些特征可用来检验两种噪声.     

Discrete Series of Su(1, 1) and Gaussian Deformation

Starting from the holomorphic discrete series of SU(1, 1), we construct a hyperbolic analogue of a quantum mechanical harmonic oscillator with a Poincaré disc as nonlinear phase space. A Bargmann-type transform is established which interwines the real wave and complex wave representation. The probability distribution of the position observable in vacuum is calculated explicitly, it admits the Gaussian law of the ordinary harmonic oscillator as zero-curvature limit.     

Thermodynamic anomalies in the presence of general linear dissipation: from the free particle to the harmonic oscillator

A free particle coupled to a heat bath can exhibit a number of thermodynamic anomalies like a negative specific heat, reentrant classicality or a nonmonotonic entropy. These low-temperature phenomena are expected to be modified at very low temperatures where finite-size effects associated with the discreteness of the energy spectrum become relevant. In this paper, we explore in which form the thermodynamic anomalies visible in the specific heat and the entropy of the free damped particle appear for a damped harmonic oscillator. Since the discreteness of the oscillator’s energy spectrum is fully accounted for, the results are valid for arbitrary temperatures. As expected, they are in agreement with the third law of thermodynamics and indicate how the thermodynamic anomalies of the free damped particle can be reconciled with the third law. Particular attention is paid to the transition from the harmonic oscillator to the free particle when the limit of the oscillator frequency to zero is taken.     

Quantum Brownian motion and the second law of thermodynamics

We consider a single harmonic oscillator coupled to a bath at zero temperature. As is well-known, the oscillator then has a higher average energy than that given by its ground state. Here we show analytically that for a damping model with arbitrarily discrete distribution of bath modes and damping models with continuous distributions of bath modes with cut-off frequencies, this excess energy is less than the work needed to couple the system to the bath, therefore, the quantum second law is not violated. On the other hand, the second law may be violated for bath modes without cut-off frequencies, which are, however, physically unrealistic models. An erratum to this article is available at .     

基态球谐振子的空间“塌陷”

用幂级数方法研究球谐振子定态薛定谔方程解析解，发现波函数球系表示ψ(r,θ，φ)在r～0处可以无界，只要rψ(r,θ，φ)在r～0处有界，就不违背波函数的玻恩统计解释而且基态能量是ω/2, 而不是3ω/2，这是低能量条件下的振动系统空间“塌陷”现象. 关键词： 球谐振子 基态能量 波函数 空间塌陷     

周期外力对频率涨落的过阻尼谐振子所作的功和能量随机共振

研究了周期外力对频率涨落的过阻尼谐振子系统作功的特点. 结果揭示了瞬时功率随时间的周期变化出现不对称性. 研究结果还揭示周期外力一个周期对系统所做的功随乘法噪声强度的变化出现非单调行为, 系统是否出现能量随机共振与抑制并存, 由乘法噪声与加法噪声之间互关联的符号决定. 关键词： 过阻尼谐振子 频率涨落 周期外力作功 能量随机共振与抑制     

Geometric Structures of Fractional Dynamical Systems in Non‐Riemannian Space: Applications to Mechanical and Electromechanical Systems

Based on a non‐Riemannian treatment of geometric objects, the geometric structures of fractional‐order dynamical systems are investigated. A fractional derivative describes non‐local effects across a space or a history encoded in memory features of the system. A system of fractional‐order differential equations is formulated in film space that includes fictitious forces. Film space is a geometric space whose coordinates comprise time, and the geometric quantities vary in time. Fractional‐order torsion tensors that appear are related to the dissipated energy and the energy conversions between subsystems and power of the system. The geometric treatment is then applied to damped‐harmonic and fractional oscillators and the hybrid electromechanical Rikitake system. The damped‐harmonic oscillator is characterized by two torsion tensors, whereas the fractional oscillator is characterized by one torsion tensor. Herein, the fractional order of the derivative of the metric tensor is used to characterize the damping of the fractional oscillator. The energy conversions between electromechanical subsystems in the Rikitake system are characterized by the torsion tensor. These results suggest that the non‐Riemannian geometric objects can represent the non‐local properties of fractional‐order dynamical systems.     

On the behavior of an oscillator clock near the singularity of a gravitational field

In 1975 Møller tried to show that the general relativistic concept of standard time or proper time would lose its physical meaning in the vicinity of singularities of a gravitational field [1]. His treatment of a classical harmonic oscillator clock falling into a singularity is checked in the present paper and is found to be insufficient to prove the above statement. A relativistic clock model is given to ensure the reasonable physical meaning of proper time.     

幂坐标矩阵元通式中的求和重数

对于一维谐振子、三维各向同性谐振子和氢原子这三个量子体系，本用逐次分部积分法给出了幂（径向）坐标矩阵元的新通式，并论证在这三类通式中所需的示放重数分别为１，１和２。     

三维各向同性谐振子的守恒张量及其轨道方程

从牛顿第二定律出发，得到了三维各向同性谐振子的守恒张量，证明了守恒张量能提供一个独立的常数，并运用守恒张量的分量表示谐振子的运动方程，铁道平面方程，长轴和短轴所在直线方程及新坐标系下的轨道方程。     

Diode-pumped 250-W zigzag slab Nd:YAG oscillator amplifier system

A laser-diode-pumped zigzag slab Nd:YAG master oscillator power amplifier (MOPA) system featuring high pulse energy and high average power was developed for pumping of an ultrashort-pulse laser system. The MOPA system consists of an oscillator, a preamplifier, two postamplifiers, and image-relay telescopes. The postamplifiers have an angle-multiplexed ring-type double-pass configuration. A pulse energy of 1.26 J and an average power of 251 W were obtained at a repetition rate of 200 Hz. The frequency-doubled power when a LiB(3)O(5) crystal was used was 105 W at a repetition rate of 170 Hz. The intensity profiles of the fundamental and the second harmonic are nearly top-hat shaped and are suitable for pumping.     

Schwinger action principle via linear quantum canonical transformations

We have applied the Schwinger action principle to general one-dimensional (1D), time-dependent quadratic systems via linear quantum canonical transformations, which allowed us to simplify the problems to be solved by this method. We show that while using a suitable linear canonical transformation, we can considerably simplify the evaluation of the propagator of the studied system to that for a free particle. The efficiency and exactness of this method is verified in the case of the simple harmonic oscillator. This technique enables us to evaluate easily and immediately the propagator in some particular cases such as the damped harmonic oscillator, the harmonic oscillator with a time-dependent frequency, and the harmonic oscillator with time-dependent mass and frequency, and in this way the propagator of the forced damped harmonic oscillator is easily calculated without any approach. PACS 02.30.Xx, 03.65.-w, 03.65.Ca     

Quantum harmonic oscillator with time-dependent mass and frequency

The quantum harmonic oscillator with time-dependent mass and frequency is analyzed by using the canonical transformation method. The varying mass and frequency of the system are reduced to constant mass and frequency, and the corresponding eigenvalues and eigenvectors are derived. The exact time-dependent coherent state of the harmonic oscillator is constructed and shown to be equivalent to the squeezed state. Damped harmonic oscillators with different frictions and forced time-dependent harmonic oscillators are also discussed.     

H-Theorem in an Isolated Quantum Harmonic Oscillator

We consider the H-theorem in an isolated quantum harmonic oscillator through the time-dependent Schrödinger equation. The effect of potential in producing entropy is investigated in detail, and we found that including a barrier potential into a harmonic trap would lead to the thermalization of the system, while a harmonic trap alone would not thermalize the system. During thermalization, Shannon entropy increases, which shows that a microscopic quantum system still obeys the macroscopic thermodynamics law. Meanwhile, initial coherent mechanical energy transforms to incoherent thermal energy during thermalization, which exhibiting the decoherence of an oscillating wave packet featured by a large decreasing of autocorrelation length. When reaching thermal equilibrium, the wave packet comes to a halt, with the density distributions both in position and momentum spaces well-fitted by a microcanonical ensemble of statistical mechanics.     

基于小型制冷机的高温超导3mm波段谐波混频

高温超导混频器具有灵敏度和谐波次数高、所需的本振和微波信号功率小、噪声低、工作频带宽等诸多优点.利用小型制冷机制冷有利于高温超导器件的应用.我们设计了与小型制冷机配套的高温超导混频系统,采取一些抑制系统噪声的措施.在该系统上成功实现了高温超导混频器在3毫米波段的50次谐波混频.     

双波量子理论中的守恒定律

研究了双波量子理论中守恒定律的数学形式,讨论了三维各向同性谐振子的守恒量及其经典极限.结果表明,双波量子理论中的守恒定律适用于单个粒子,而通常量子力学中的守恒定律仅适用于统计系综. 关键词：