Quantum damped harmonic oscillator on non-commuting plane

In the present paper we study the quantum damped harmonic oscillator on non-commuting two-dimensional space. We calculate the time evolution operator and we find the exact propagator of the system. We investigate as well the thermodynamic properties of the system using the standard canonical density matrix. We find the statistical distribution function and the partition function. We calculate the specific heat for the limiting case of critical damping, where the frequencies of the system vanish. Finally we study the state of the system when the phase space of the second dimension becomes classical. We find that these systems have some singularities and zeros for low temperatures.     

Quantum theory of the damped harmonic oscillator

A phenomenological stochastic modelling of the process of thermal and quantal fluctuations of a damped harmonic oscillator is presented. The divergence of the momentum dispersion associated with the Markovian limit is removed by a Drude regularization. The variances of position and momentum are evaluated in closed form at arbitrary temperature and for arbitrary damping. Properties of real and imaginary time correlation functions are discussed, and a spectral decomposition of the equilibrium density matrix is given.     

Quantum decoherence of the damped harmonic oscillator

In the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We also calculate the decoherence time and show that it has the same scale as the time after which thermal fluctuations become comparable with quantum fluctuations. The text was submitted by the author in English.     

含时阻尼线性谐振子的量子不变量处理

在适当的正则化变换下,采用Lewis-Riesenfeld量子不变量理论,得到了含时阻尼线性谐振子的精确波函数,波函数的正确性和普遍性同样得到讨论.     

Quantum mechanical masterequation and Fokker-Planck equation for the damped harmonic oscillator

For the statistical operator of the damped harmonic oscillator a Masterequation is given in operator form describing both inelastic and elastic, purely phase destroying processes. By expressing the statistical operator in the diagonal representation with respect toGlauber's coherent states the Masterequation is transformed into a Fokker-Planck equation forGlauber's quasiprobability distribution function. The general solution of this Fokker-Planck equation is calculated. It is shown how the solution of a Masterequation can be used for calculating correlation functions and expressions are given for the amplitude and intensity correlation functions which are in complete formal agreement with the corresponding classical formulae.     

Quantum damped oscillator II: Bateman’s Hamiltonian vs. 2D parabolic potential barrier

We show that quantum Bateman’s system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that this system displays the family of complex eigenvalues corresponding to the poles of analytical continuation of the resolvent operator to the complex energy plane. It is shown that this representation is more suitable than the hyperbolic one used recently by Blasone and Jizba.     

Quantum proximity resonances

The zero-range potential approximation is used to show that quantum proximity resonances discussed recently by Heller [Phys. Rev. Lett. 77 (1996) 4122] may also occur in the absence of single-scatterer resonances. It is argued that for two identical scatterers a resonant structure appears in the Σ_u-wave rather than in the P-wave partial cross section.     

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.     

Coherent states of a damped harmonic oscillator

We construct here the coherent states (annihilation operator eigenstates) of a damped harmonic oscillator. These coherent states, which are normalizable, have the desired behaviour in the classical limit (ℏ→0).     

Canonical quantization of the Bateman-Morse-Feshbach damped oscillator

The Bateman-Morse-Feshbach classical formulation of the damped oscillator is canonically quantized. The spectrum of the Hamiltonian is given. It is shown that the wavefunctions behave asymptotically as a superposition of damped oscillators when their initial values belong to an appropriately-selected dense subset of the Hilbert space.partially supported by U.S. Army Grant DAAL03-87-K-0110.Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy.     

Exact green function of a damped oscillator

The explicit Green functions for a damped oscillator with an arbitrary time-dependent frequency and a perturbative force are obtained in coordinate and coherent states representation. This illustrates the application of a general method for the construction of Green functions based on the employment of the integrals of the motion of quantum systems.     

一类线性阻尼振子的随机共振研究

针对随机有色噪声参数激励和周期调制噪声外激励联合作用下的线性阻尼振子,利用Shapiro-Loginov公式推导了系统响应的一、二阶稳态矩的解析表达式.发现这类系统存在传统的随机共振、广义的随机共振和“真正”的随机共振;当乘性噪声强度和调制噪声强度的比值大于等于1时,系统出现随机多共振现象.通过数值计算的系统响应功率谱,验证了理论分析结果. 关键词： 随机共振 周期调制的噪声 线性阻尼振子     

Quantum Bouncer with Dissipation

Effects on the spectra of the quantum bouncer due to dissipation are given when a linear of quadratic dissipation is taken into account. Classical constants of motions and Hamiltonians are deduced for these systems and their quantized eigenvalues are estimated through perturbation theory. Differences were found comparing the eigenvalues of these two quantities.     

Symmetries and conservation laws of the damped harmonic oscillator

We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have studied the variational or Noether symmetries of the damped harmonic oscillator representing it by an explicitly time-dependent Lagrangian and found that a five-parameter group of transformations leaves the action integral invariant. Amongst the associated conserved quantities only two are found to be functionally independent. These two conserved quantities determine the solution of the problem and correspond to a two-parameter Abelian subgroup.      

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.     

量子无规运动与核耗散

从动力学对称性观点出发考察了量子规则运动与无规运动 .用能级动力学研究了从量子规则运动向量子无规运动的过渡 ,给出了导致能级混沌的条件 ,揭示了造成能级混沌的机制 .用混沌态矢的特征解释了原子核的各态历经集体态的衰变特性 .研究了重离子碰撞中核耗散与动力学对称性破坏之间的关系. Quantum regular and irregular motions are investigated from the viewpoint of dynamical symmetry. The transition from quantum regular motion to chaotic motion is studied by level dynamics and computer experiments. The conditions for onset of quantum chaos are presented.The mechanism for causing chaotic level spectrum is unveiled. The decay behavior of the nuclear ergodic collective states is explained in terms of the peculiar property of chaotic states. The connection between nuclear...     

A method of treatment the damped quantum oscillator

A functional-integration method allowing to treat the damped quantum oscillator in equilibrium without making special choice of the heat-bath Hamiltonian is introduced. Exact results for the damped quantum oscillator calculated recently are shown to represent a special case of the present treatment.