用动力学方法研究原子分子碰撞过程中的统计平均问题

动力学李代数方法在研究原子分子碰撞问题中是一种很重要的方法.在计算过程中我们用密度算子导出了物理量的统计平均值.同时我们用时间演化算子计算了振转能量的跃迁几率.作为例子我们用此方法计算了H2和He的碰撞问题.     

场频率变化时多光子J-C模型中原子的动力学特性

利用多光子J-C模型,在旋波近似下,研究了场频率随时间变化时二能级原子通过多光子跃迁与单模辐射场相互作用系统中原子的动力学特性,分析了光场频率随时间以正弦函数形式作小量变化的典型情况,利用数值计算方法给出原子算符S3(t)平均值随时间的演化曲线.研究结果表明:原子算符S3(t)平均值随时间的演化受场频率随时间正弦函数形式变化的调制,场频率振荡的幅值u越大调制作用越强.     

非线性介观电路中的崩塌与回复现象

对非线性介观电路中电流的量子动力学行为进行研究.研究表明:由于非线性双向二极管的影响,使得在非线性介观电路中电流的平均值随时间变化存在被调制的现象.即在非线性介观电路中电流的平均值随时间变化存在周期性的崩塌与回复现象,并讨论了参数的变化对这种调制的现象的影响.     

Student’s t分布及其在实验数据处理中的应用

引言在数据分析中经常遇到这样两方面的问题,即具有正态分布的随机变量(如带有偶然误差的某个物理量的测量值),经过多次测量,它的平均值的误差是多少?或是同一物理量由两个人或两种设备分别测出两组数据,这两组数据的平均值不相同,这时需要推断出一个结论:这两个平均值的差别到底是统计涨落引起的,还是其中一个或两个由某种系统误差引起的。如果该统计量的总体方差σ~2已知的话,     

1+1维抛射沉积模型内部结构动力学行为的数值研究

采用Kinetic Monte Carlo方法对1+1维抛射沉积(BD)模型内部结构的动力学行为进行了大量的数值模拟研究.分别分析了空洞密度和内部界面的动力学行为.研究表明,空洞密度呈高斯型分布,其平均值首先随生长时间快速增长,然后达到一个与基底尺寸无关的饱和值.除表面宽度,还引入了新的极值统计方法来分析该模型内部界面的动力学行为,分析结果显示,1+1维BD模型内部界面的演化满足标准的Family-Vicsek标度规律,并且属Kardar-Parisi-Zhang方程所描述的普适类.最后对表面宽度和极值统计两种理论方法的有限尺寸效应进行了比较.     

光束通量空间分布随机变化的统计分析

基于高功率激光装置研究了大口径激光束通量空间分布随机变化的统计规律.统计分析表明,多发次累积的光束最大通量分布服从高斯分布,平均值随累积发次的增加而上升,但标准差保持不变,与单发次光束通量分布的标准差基本一致.这一统计规律是由大口径光束通量空间分布的大面相似性和局域差异性所决定的.     

具有半单李代数结构的线性非自治量子系统的精确解

给出了对于具有半单李代数结构的线性量子系统求其精确解的代数动力学方法. 这个方法通过一系列规范变换,把哈密顿量逐步简化为Cartan算子的函数. 规范变换的系数由一组常微分方程确定,Schrodinger方程的完全解通过这组规范变换的逆变换得到.与此同时,还可以得到一组与时间有关的动力学不变量. 作为例子,又具体求解了一个SU(3)模型.     

二维随机介质中的能量分布和频谱特性

研究了二维随机介质中能量的空间分布和一些特定区域的频谱特性.结果显示介质中能量呈局域化分布,其分布与介质中颗粒的随机分布有关,还与激发光的波长有密切的关系,介质中能量聚集的区域和介质的准封闭区域有一定关系但并非一一对应.所考察的各准封闭区域的频谱均随时间变化,在同一激发光的激励下各准封闭区域的频谱均不相同,而同一区域在不同的激发光的激励下频谱也不相同.当激发波长与准封闭区域的结构参数偏差较大时,频谱中谱峰会出现此消彼涨的模式竞争现象,而且能量衰减得较快;而当激发波长与该结构参数较接近时,相应的频谱中存在一 关键词： 激光物理 有限时域差分法 局域化 频谱特性     

麦克斯韦-玻尔兹曼分布在易辛模型中的应用

麦克斯韦-玻尔兹曼分布给出了系统在任一微观状态下的玻尔兹曼概率,从而可以计算系统中宏观观测量的统计平均值.但在实际计算中,由于系统可能微观状态数随系统晶格格点数增大而指数增大,往往无法进行计算.本文以易辛模型为例,介绍了如何从玻尔兹曼概率的角度研究系统可能微观状态的演化过程,从而可以只考虑高概率的微观状态.使用该方法,研究了二维易辛模型的平均每自旋的基态能量和平均每自旋的磁化率随温度的变化关系.     

量子条件振幅算子性质的研究

分析量子条件振幅算子的性质，该算子起一个类似于在经典信息理论中的条件概率的作用.论证表示一个量子双组元系统的条件算子的频谱在局域幺正变换下是不变的，并且表明它的不可分性.证明一个可分态的条件振幅算子不能有一个超过1的本征值.得出一个在von Neumann条件熵的非负性基础上的相关的可分性条件. 关键词： 条件概率 条件振幅算子 von Neumann条件熵 可分性条件     

A new approach for the justification of ensembles in quantum statistical mechanics — I

In this and the following paper, a new approach for the justification of ensembles in statistical mechanics is given. The essential physical idea is that a measurement is an average of values arising from disjoint regions in three-space. This idea is given a mathematical basis in terms of a class of operators called local operators, and the first paper is devoted primarily to the development of the properties of local operators. In particular, a complete characterization of the bounded local operators on ₂ spaces of finite measure is given. Two results of importance for statistical mechanics are also derived. First, it is shown that the observables of quantum mechanics are local operators. Second, it is shown that the expectation value of an observable for a pure state can be written formally as an ensemble average. In the following paper, these results are used to develop a new approach for the justification of statistical ensembles.This work was supported in part by research grants from the National Science Foundation and the U.S. Public Health Service. The material of this paper is contained in a doctoral dissertation submitted by the author to the University of Oregon (1969).     

光场算符n次幂叠加激发混沌场的量子特性

构造了光场算符n次幂叠加激发混沌场,采用数值计算方法研究了该量子态的压缩效应、反聚束效应和统计性质,讨论了混沌场平均光子数、算符叠加系数及其幂次n对量子特性的影响.研究结果表明:光场算符n次幂叠加激发混沌场不呈现压缩效应,但呈现出反聚束效应和亚泊松分布性质,并且随平均光子数增大,它的反聚束效应和亚泊松分布性质减弱;随着算符组合部分中产生算符的比重增大,光场反聚束效应和亚泊松分布性质增强;随着算符幂次增大,亚泊松分布性质加强.     

Quantum Dynamics and Kinematics from a Statistical Model Selected by the Principle of Locality

Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of local causality. By contrast, here we shall show that the Schrödinger equation with Born’s statistical interpretation of wave function and uncertainty relation can be derived from a statistical model of microscopic stochastic deviation from classical mechanics which is selected uniquely, up to a free parameter, by the principle of Local Causality. Quantization is thus argued to be physical and Planck constant acquires an interpretation as the average stochastic deviation from classical mechanics in a microscopic time scale. Unlike canonical quantization, the resulting quantum system always has a definite configuration all the time as in classical mechanics, fluctuating randomly along a continuous trajectory. The average of the relevant physical quantities over the distribution of the configuration are shown to be equal numerically to the quantum mechanical average of the corresponding Hermitian operators over a quantum state.     

Quantum statistical dynamics: Statistics origin,measurement, and irreversibility

It is shown that in the quantum theory of systems with a finite number of degrees of freedom which employs a set of algebraic states, a statistical element introduced by averaging the mean values of operators over the distribution of continuous quantities (a spectrum point of a canonical operator and time) is conserved for the limiting transition to the distribution. On that basis, quantum statistical dynamics, i.e., a theory in which dynamics (time evolution) includes a statistical element, is advanced. The theory is equivalent to orthodox quantum mechanics as regards the orthodox states, but is essentially different with respect to the coherence properties in a continuous spectrum. The measurement-process theory, including the statistical interpretation of quantum mechanics, and the irreversibility theory are constructed, and the law of increasing chaos, which is a strengthening of the law of entropy increase, is obtained. In our theory, mechanics and statistics are organically connected, whereby the fundamental nature of probabilities in quantum physics manifests itself.     

Lifetime distributions in the methods of non-equilibrium statistical operator and superstatistics

A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter – the lifetime of a system. Superstatistics, introduced in works of Beck and Cohen [Physica A 322, 267 (2003)] as fluctuating quantities of intensive thermodynamical parameters, are obtained from the statistical distribution of lifetime (random time to the system degeneracy) considered as a thermodynamical parameter. It is suggested to set the mixing distribution of the fluctuating parameter in the superstatistics theory in the form of the piecewise continuous functions. The distribution of lifetime in such systems has different form on the different stages of evolution of the system. The account of the past stages of the evolution of a system can have a substantial impact on the non-equilibrium behaviour of the system in a present time moment.     

Multi—mode q—oscillator algebras with q^2（k＋1）=1 and related thermo field dynamics

A type of multi-mode q-oscillator algebra with q^2(k+1)=1 is set up and the associated q_k-thermo field dynamics is constructed for all k=1,2,…,∞ in a unified form. It is demonstrated that these q_k-thermo field dynamics can all be nicely fitted into the algebraic formulation of statistical mechanics (axiomatized form for statistical physics). This means that we obtain infinitely many realizations of the algebraic scheme, which extend the consideration of Ojima [1981 Ann. Phys. 137 1] and contain the usual thermo field dynamics for the fermionic (k=1) and bosonic (k=∞) systems as special cases. As simple applications, the q_k-statistical average of some operators are given.     

Second quantized reduced Bloch equations and the exact solutions for pairing Hamiltonian

In this article, we present a set of hierarchy Bloch equations for the reduced density operators in either canonical or grand canonical ensembles in the occupation number representation. They provide a convenient tool for studying the equilibrium quantum statistical mechanics for some model systems. As an example of their applications, we solve the equations for the model system with a pairing Hamiltonian. With the aid of its symplectic group symmetry, we obtain the statistical reduced density matrices with different orders. As a special instance for the solutions, we also get the reduced density matrices of the ground state for a superconductor.