阻尼自由振荡电路的量子力学处理

本文首先将阻尼谐振子量子化，然后利用机电模拟方法实现了阻尼自由振荡电路的量子化。     

含时阻尼谐振子的传播子与严格波函数

通过正则化变换技巧,寻找到一种对阻尼系数随时间变化的阻尼谐振子直接量子化方案,进而采用高斯型传播子和费曼路径积分方法求出了含时阻尼谐振子的严格波函数,并对波函数的普遍意义,坐标和动量的零点涨落以及两者的不确定关系作了讨论 关键词： 含时阻尼 传播子 费曼路径积分     

介观压电石英晶体等效电路的量子化

借鉴阻尼谐振子作量子力学处理的研究思想,将介观压电石英晶体等效电路量子化,在此基础上研究了真空态和压缩真空态下,各支路电流和电压的量子涨落. 关键词： 介观压电石英晶体 等效电路 阻尼谐振子 量子涨落     

RLC介观电路中的量子涨落

从线性谐振子哈氏量出发,通过正则变换,得到了受迫阻尼谐振子哈氏量,还讨论了在压缩态下的电荷和电流的量子涨落。     

阻尼谐振子到简谐振子的变换

在牛顿力学、拉格朗日力学和哈密顿力学3种形式中,利用变量变换将阻尼谐振子变换成简谐振子.     

阻尼谐振子的拉格朗日函数和哈密顿函数

利用一种直接方法将阻尼谐振动微分方程变换成等价的自伴随形式,并构造出阻尼振子的两个拉格朗日函数和哈密顿函数,导出了阻尼谐振子的Noether守恒量.     

巧用光电门改进阻尼振动实验

在气垫导轨上阻尼振动研究的实验中,采用两个光电门分别测量阻尼振动的谐振子振动周期和半衰期,进而求出振动系统的粘滞性阻尼常量。该方法克服了传统实验中采用电子秒表测量谐振子做阻尼振动的半衰期时,因需要人眼观察和手动操作而导致测量误差大的问题,实现了对气垫导轨的粘滞性阻尼常量较为精确的测量。     

关于线性阻尼振子第一积分的研究

通过引入一维线性阻尼振子基本积分来构造其他第一积分, 包括不含时的积分. 将这种方法推广到多维情形, 构造二维和n维线性阻尼振子不同形式的第一积分; 证明不同类型的二维线性阻尼振子都存在三个独立的不含时的第一积分, n维线性阻尼振子存在2n-1个独立的不含时的第一积分. 利用变量变换将线性阻尼振子的第一积分变换成简谐振子形式的第一积分. 关键词： 线性阻尼振子 第一积分 基本积分 简谐振子     

介观互感耦合阻尼LC并联电路的量子化能谱

对介观互感耦合阻尼并联LC电路作双模耦合阻尼谐振子处理,将其量子化,通过三次幺正变换,将体系的哈密顿量对角化,在此基础上给出了体系的能谱。     

高Q值半球谐振子精密加工技术研究

半球谐振子的机械能量损耗包括材料本征损耗、空气阻尼损耗、支撑损耗、热弹性损耗和表面损耗等,直接影响了半球谐振子Q值。通过分析这些能量损耗的数学模型,总结出半球谐振子的关键技术指标是材料性能、形位精度和表面粗糙度。综合考虑半球谐振子的精度和工程化应用,提出了一套高精度半球谐振子加工工艺,经过精密磨削、精密抛光和化学抛光后,加工得到的谐振子球面圆度小于0.25μm,表面粗糙度小于15 nm,品质因数大于5.2×107。对高精度半球谐振子加工和半球谐振陀螺制造工程化具有重要的指导意义。     

Approach to the quantum evolution for underdamped, critically damped, and overdamped driven harmonic oscillators using unitary transformation

Exact solution of the Schrödinger equation is derived for underdamped, critically damped, and overdamped harmonic oscillators with a driving force. A unitary operator transforming Hamiltonian into a simple form is introduced. The transformed Hamiltonian, represented in terms of a modified frequency ω, is identical with the Hamiltonian of the standard harmonic oscillator for the underdamped oscillator, with the Hamiltonian of a free particle for the critically damped oscillator, and with the Hamiltonian of a system with a harmonic parabolic potential for the overdamped oscillator. The eigenvalues of underdamped oscillator are discrete while those of the critically damped and the overdamped oscillators are continuous.     

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     

Time Dependence of Joint Entropy of Oscillating Quantum Systems

The time dependent entropy (or Leipnik’s entropy) of harmonic and damped harmonic oscillator systems is studied by using time dependent wave function obtained by the Feynman path integral method. The Leipnik entropy and its envelope change as a function of time, angular frequency and damping factor. Our results for simple harmonic oscillator are in agreement with the literature. However, the joint entropy of damped harmonic oscillator shows remarkable discontinuity with time for certain values of damping factor. The envelope of the joint entropy curve increases with time monotonically. These results show the general properties of the envelope of the joint entropy curve for quantum systems.     

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.     

A comment on quantum-mechanical damping

The question of introducing damping into quantum mechanics has come into prominence again. It is argued, from previous experience with the damping of a harmonic oscillator, that it is easy to violate the uncertainty principle, particularly if it is overlooked that absorbers are also emitters. The usual classical equations for a damped system are those for a smoothed variable, with the noise fluctuations subtracted. In the case of a damped harmonic oscillator the process of subtracting the noise and so defining a smoothed variable was examined many years ago, and to some extent can be used to justify present practice.     

Quantum damped oscillator I: Dissipation and resonances

Quantization of a damped harmonic oscillator leads to so called Bateman’s dual system. The corresponding Bateman’s Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding generalized eigenvectors may be interpreted as resonant states which are responsible for the irreversible quantum dynamics of a damped harmonic oscillator.     

Linear and nonlinear resonance features of an erbium-doped fibre ring laser under cavity-loss modulation

The continuous-wave output of a single-mode erbium-doped fibre ring laser when subjected to cavity-loss modulation is found to exhibit linear as well as nonlinear resonances. At sufficiently low driving amplitude, the system resembles a linear damped oscillator. At higher amplitudes, the dynamical study of these resonances shows that the behaviour of the system exhibits features of a nonlinear damped oscillator under harmonic modulation. These nonlinear dynamical features, including harmonic and subharmonic resonances, have been studied experimentally and analysed with the help of a simple time-domain and frequency-domain information obtained from the output of the laser. All the studies are restricted to the modulation frequency lying in a regime near the relaxation oscillation frequency.     

A complex symplectic model for the damped oscillator

The linearly damped harmonic oscillator is described by a hamiltonian complex manifold. The master equation for the complex eigenstates of the quantized hamiltonian is found.