Universal statistical properties of drift-interchange turbulence in TORPEX plasmas

A unique parabolic relation is observed to link skewness and kurtosis of around ten thousand density fluctuation signals, measured over the whole cross section of a toroidal magnetized plasma for a broad range of experimental conditions. All the probability density functions of the measured signals, including those characterized by a negative skewness, are universally described by a special case of the Beta distribution. Fluctuations in the drift-interchange frequency range are necessary and sufficient to assure that probability density functions can be described by this specific Beta distribution.     

A statistical test of Anderson localization

Numerical demonstrations of localization in random systems are difficult to obtain and interpret because of statistical fluctuations in the electron probability density. This difficulty can be avoided through the use of correlation functions defined in terms of the electron probability density. The fluctuations can then be eliminated by averaging over a large number of Anderson Hamiltonians. The resulting averaged correlation functions clearly show that electrons are exponentially localized. The localization demonstrated here is sufficient to insure a zero dc conductivity in the limit of large systems.     

Nonstandard Boundary Conditions in Quantum Mechanics

The class of boundary conditions for wave functions which follow from the quantum mechanical continuity equation for the probability density and the probability current is considered.     

Polarized light

Following the recent work of Chandleret al on quasi probability distributions for spin-1/2 particles, we show that polarized light can be interpreted in terms of trivariate probability distributions in two different ways by choosing the variates to correspond to (i) the co-ordinates on the Poincare sphere, (ii) the components of the spin operator of the photon. In either case, it is shown that the Margenau-Hill procedure leads to probability mass functions while the Wigner-Weyl approach leads to probability density functions and the well-known Stokes parameters are also realised as appropriate averages with respect to these distribution functions.     

Error statistics in a high-rate communication line with bit-density optimization

Direct effective numerical simulation is used to determine the tails of probability density functions of marks and spaces and the error statistics in the optical communication line based on a conventional single-mode fiber and a dispersion-compensation fiber with a reduced density of marks in the original bit sequence. Simple analytical approximations for the tails of the probability density function are derived to determine the number of errors in the line with a relatively high accuracy.     

A macro traffic flow model with probability distribution function

In this paper, we introduce three probability distribution functions into the dynamic equation and propose a macro traffic flow model to investigate the impacts of the probability distribution functions on the evolutions of traffic flow under three typical states (i.e., uniform flow, shock, rarefaction wave, and small perturbation). The numerical results indicate that the probability distribution functions do not change the density and speed distributions of uniform flow, produce a two-layer shock but have no prominent effects on rarefaction wave, and have little effect on small perturbation.     

Integro-differential equation for joint probability density in phase space associated with continuous-time random walk

We derive an integro-differential equation for the joint probability density function in phase space associated with the continuous-time random walk, with generic waiting time probability density function and external force. This equation permits us to investigate whole diffusion processes covering initial-, intermediate-, and long-time ranges, which can distinguish the evolution details for systems having the same behavior in the long-time limit with different initial- and intermediate-time behaviors. Moreover, we obtained analytic solutions for probability density functions both in velocity and phase spaces, and interesting dynamic behaviors are discovered.     

Finite element distributions in statistical theory of energy levels in quantum systems

The probability density functions of the three-point finite elements of the three adjacent energy levels for the three-level quantum system are introduced as a supplementary characteristics of quantum chaos. The three-level quantum system is studied. The probability density functions of the second difference and asymmetrical three-point first finite element are computed for the three-dimensional Gaussian orthogonal ensemble GOE(3), the three-dimensional Gaussian unitary ensemble GUE(3), the three-dimensional Gaussian symplectic ensemble GSE(3), as well as for the Poisson ensemble PE.     

A wave function for stock market returns

The instantaneous return on the Financial Times-Stock Exchange (FTSE) All Share Index is viewed as a frictionless particle moving in a one-dimensional square well but where there is a non-trivial probability of the particle tunneling into the well’s retaining walls. Our analysis demonstrates how the complementarity principle from quantum mechanics applies to stock market prices and of how the wave function presented by it leads to a probability density which exhibits strong compatibility with returns earned on the FTSE All Share Index. In particular, our analysis shows that the probability density for stock market returns is highly leptokurtic with slight (though not significant) negative skewness. Moreover, the moments of the probability density determined under the complementarity principle employed here are all convergent — in contrast to many of the probability density functions on which the received theory of finance is based.     

Calculation of error probability in an optical communication channel in the presence of intersymbol interference,using a characteristic function method

In this paper the error rate of an optical channel is calculated. The channel considered consists of a laser or light emitting diode as the optical source and a glass fibre as transmission medium. The transmitted optical pulses are spread in the fibre causing intersymbol interference. The receiver is assumed to be an avalanche photodiode which is considered as a p-n junction and a random multiplier whose electron probability distribution function is known, and a filter. In calculating the probability of error, their characteristic functions are multiplied and the probability density function of all the noises put together is truncated to a finite interval and described in a trigonometric series form. The total characteristic function is related to the Fourier coefficients of the periodic probability density function, resulting in an expression that is then used, for a given bit rate, to determine the worst case and average probability of error as functions of transmitted power or signal-to-noise ratio, for different amounts of intersymbol interference.     

Analysis of wetting layer effect on electronic structures of truncated-pyramid quantum dots

We carry out a theoretical analysis of wetting layer effect on band-edge profiles and electronic structures of InAs/GaAs truncated-pyramid quantum dots, including the strain effect. A combination of an analytical strain model and an eight-band Fourier transform-based k · p method is adopted in the calculation. Strain modified band-edge profiles indicates that wetting layer widens the potential well inside the dot region. Wetting layer changes ground-state energy significantly whereas modifies probability density function only a little. The main acting region of wetting layer is just underneath the base of the dot. Wetting layer redistributes probability density functions of the lowest electron state and probability density functions of highest hole state differently because of the different action of quantum confinement on electrons and holes.     

Probability density functions for hyperbolic and isodiachronic locations

Animal locations are sometimes estimated with hyperbolic techniques by estimating the difference in distances of their sounds between pairs of receivers. Each pair specifies the animal's location to a hyperboloid because the speed of sound is assumed to be spatially homogeneous. Sufficient numbers of intersecting hyperboloids specify the location. A nonlinear method is developed for computing probability density functions for location. The method incorporates a priori probability density functions for the receiver locations, the speed of sound, winds, and the errors in the differences in travel time. The traditional linear approximation method overestimates bounds for probability density functions by one or two orders of magnitude compared with the more accurate nonlinear method. The nonlinear method incorporates a generalization of hyperbolic methods because the average speed of sound is allowed to vary between different receivers and the source. The resulting "isodiachronic" surface is the locus of points on which the difference in travel time is constant. Isodiachronic locations yield correct location errors in situations where hyperbolic methods yield incorrect results, particularly when the speed of propagation varies significantly between a source and different receivers.     

窄带随机噪声作用下Duffing振子的双峰稳态概率密度

研究了Duffing振子在窄带随机噪声激励下的系统响应的双峰稳态概率密度问题.用多尺度法 分离了系统的快变项，得到了系统慢变项满足的随机微分方程.用线性化方法求出了双峰稳 态概率密度的表达式.数值模拟表明本文提出的方法是有效的. 关键词： Duffing振子 双峰稳态概率密度 多尺度法 线性化方法     

Uncertainties induced by statistical fluctuations in fast monoenergetic neutron yield measurements

A plastic scintillation detector was used to measure the yield of deuterium-deuterium (DD) neutrons or deuterium-tritium (DT) neutrons. Collisions of fast neutrons with hydrogen nucleus in a scintillator generated recoil protons, the energies of which were fully deposited in the scintillator. The statistical fluctuation of the protons' number and that of the protons' total energy were two sources of measurement uncertainty. Based on DT neutrons, this paper represents the algorithms of computing the probability density functions of the two sources. Uncertainties of the measurement induced by statistical fluctuations were finally computed by constructing the probability density functions of the proton number and that of the neutron number.     

Statistical properties of N random sinusoidal waves in additive Gaussian noise

The first order probability density functions of the sums of N independent sinusoidal waves having random amplitudes and phases in additive Gaussian noise are studied for the cases where N is fixed and where N in Poisson distributed. The conditional moments about the origin are obtained in closed form or both situations. The corresponding probability density functions for the envelope are also studied. The even conditional moments about the origin are also obtained in closed form. Representative numerical results are presented.     

Functional Lévy walks

The problem of finding the probability distribution function for a random variable which is the function of a random walking radius vector is analyzed. It is shown for a wide class of these functions hyperbolically dependent on the value of the radius vector that the probability density distributions of these random variables are the known Lévy functions. The conditions under which functional Lévy walks pass into truncated ones are considered.     

Condition for any realistic theory of quantum systems

In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of physical quantities is evaluated by means of a probability distribution. We study the possibility to describe pure quantum states and events with classical probability distributions and conditional probabilities and prove that the distributions have to be nonlinear functions of the density operator. Some examples are considered. Finally, we deal with the exponential complexity problem of quantum physics and introduce the concept of classical dimension for a quantum system.     

An intermediate distribution between Gaussian and Cauchy distributions

In this paper, we construct an intermediate distribution linking the Gaussian and the Cauchy distribution. We provide the probability density function and the corresponding characteristic function of the intermediate distribution. Because many kinds of distributions have no moment, we introduce weighted moments. Specifically, we consider weighted moments under two types of weighted functions: the cut-off function and the exponential function. Through these two types of weighted functions, we can obtain weighted moments for almost all distributions. We consider an application of the probability density function of the intermediate distribution on the spectral line broadening in laser theory. Moreover, we utilize the intermediate distribution to the problem of the stock market return in quantitative finance.     

Intermittency of the density fluctuations and its influence on the radial transport in the boundary of J-TEXT

To improve the understanding of the turbulence intermittency,a detailed investigation of the intermittency of the density fluctuations has been performed in the boundary of J-TEXT.The intermittency of the density fluctuations and its influence on the radial transport are reported.The probability distribution functions of the density fluctuations are not scale-invariant,being inconsistent with the self-organized criticality hypothesis.The underlying dynamics of the intermittency are detected using the quiet-time statistical method.The probability distribution function of the quiet times shows double-power-law regions,indicating the existence of correlations between the successive burst events.     

无限深势阱问题的可视化研究

基于计算软件对一些常见的无限深势阱进行了可视化研究,并设计了GUI界面实现对势阱的选择.在选定势阱后,设置好相应的势阱参数和量子数,便可依次绘制出低维势阱的波函数、概率密度函数和三维势阱中的电子云图像.文中分析了二维和三维势阱中能级的简并度问题,并重点讨论了不同势阱波函数和概率密度函数随量子数的变化规律.将势阱问题可视化可以方便分析不同条件下波函数的物理图像,有助于量子力学课程中的教师教学与学生学习.