也谈概率密度和概率流密度算符

针对<大学物理>2008年第8期上关于粒子概率密度算符和概率流密度算符的讨论一文进行了补充,对一般空间(如动量空间)中的概率和概率流进行了较系统的阐述,并纠正了该文中的有关错误论断.     

Modelling and characterization of electrostatic current noise induced mechanically in wired wearable applications

By means of statistical modelling and measurement, the triboelectric current noise spectral density is evaluated for shielded cables in body-borne wired network subjected to mechanical stresses. Assuming a shot noise model, an expression for the current spectral density of the noise is derived. The efficiency of the methodology is demonstrated by measuring the triboelectric current noise in two shielded cables subjected to bending. Thereafter the parameters of the noise pulses' waiting time and amplitude probability density functions are extracted from measurement, thus enabling the computation of the current spectral density of the noise induced mechanically in body-borne wired networks.     

The influences of the second harmonics together with the asymmetries of junctions on the voltage–current characteristics of high TC DC SQUIDs

We consider a superconducting quantum interference device having two arbitrary different over damped junctions transporting different currents. By replacing the governed two-dimensional Fokker–Planck equation with two one-dimensional equations, two density probability currents are appeared which determine the statistical average of the time-averaged total voltage across the device. To obtain the density probability currents, two coupled integral equations are introduced. These equations together with two other equations coming from normalizing conditions, found one generalized formulation for the voltage–current characteristics of the device. Based on that, the voltage–current characteristics of large inductance asymmetric DC SQUIDs having first and second harmonics in their current-phase relations are obtained and some predictions are illustrated.     

Spin anisotropy for excitation in collisions between two one-electron atoms

The singlet and triplet contributions of excitation cross sections are studied theoretically for collisions between various two one-electron atoms. The spin anisotropy is shown to have a general behavior in the important impact energy range. At low energies triplet cross sections dominate completely over the singlet ones while the opposite is true when the active electron and projectile velocities are comparable. Beyond the matching velocity regime singlet and triplet contributions become identical. We propose a general dynamical interpretation based on the analysis of the time dependency of the electron probability density and probability current density.     

Quantum mechanics as applied mathematical statistics

Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schrödinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.     

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.     

Similarity solutions of the Fokker–Planck equation with time-dependent coefficients

In this work, we consider the solvability of the Fokker–Planck equation with both time-dependent drift and diffusion coefficients by means of the similarity method. By the introduction of the similarity variable, the Fokker–Planck equation is reduced to an ordinary differential equation. Adopting the natural requirement that the probability current density vanishes at the boundary, the resulting ordinary differential equation turns out to be integrable, and the probability density function can be given in closed form. New examples of exactly solvable Fokker–Planck equations are presented, and their properties analyzed.     

A study of the interface roughness effect in Si nanowires using a full 3D NEGF approach

The effect of interface roughness in ballistic Si nanowires is investigated using a full 3D non-equilibrium Green's Functions formalism. The current density, the electron density and the transmission function are calculated for nanowires with different interface roughness configurations. Interface roughness is randomly generated using an exponential autocorrelation function. The interface roughness profile in nanowires with 2 nm diameter and 6 nm length is reflected in the current density landscape showing macroscopic 3D patterns. These macroscopic patterns affect the transmission probability causing resonances coming from the constrictions in the channel. The shape of the electron density in cross-sections along the wire follows the distortion of electron transversal wave function.     

The repulsive nature of naked singularities from the point of view of Quantum Mechanics

We use the Dirac equation coupled to a background metric to examine what happens to quantum-mechanical observables like the probability density and the radial current in the vicinity of a naked singularity of the Reissner–Nordström type. We find that the wave function of the Dirac particle is regular in the point of the singularity. We show that the probability density is exactly zero at the singularity reflecting quantum-mechanically the repulsive nature of the naked singularity. Furthermore, the surface integral of the radial current over a sphere in the vicinity of the naked singularity turns out to be also zero.     

Dynamics of superconducting qubits with exactly solvable bias pulses

The dynamics of a quantum two-state system (qubit) with external control bias pulses of special shapes is considered. The bias pulses represent the potentials for which the Schrödinger equation can be solved exactly. The probability to register a definite direction of the current in a loop and its time-averaged values are calculated for the flux qubit; calculations are performed both analytically and numerically in the presence of relaxation and decoherence within the framework of the density matrix formalism. It is demonstrated that there exist external bias pulses for which the definite current direction probability is a monotonically increasing function of time that approaches a limiting value exceeding 1/2. The probability to find the system in the excited state is calculated, and the possibility of inverse population in a properly driven two-state system is demonstrated given that the relaxation and decoherence rates are small enough.     

Thermoemission of Eu ions and its fluctuations

The surface ionization of europium on tungsten has been studied using a single filament ion source in a 90° magnetic mass spectrometer. The influence of temperature on the ion current was measured between 1100 and 2800 K. Additionally, the ion current noises arising from the fluctuations of the work function as a result of random fluctuations of the adsorbate density on the ion emitter surface has been investigated. The spectral density functions and their temperature dependence are discussed in terms of the surface diffusion noise model at adsorption-desorption equilibrium. The density probability function seems to be Gaussian and its skewness Sk and kurtosis Ex were: Sk 0, Ex 3.     

Tunnelling across a potential barrier

Generalized expressions for the tunnelling probability spectrum and the tunnelling time are derived for a potential barrier of arbitrary shape independent of the use of the perturbation theory. A method to obtain the tunnelling current density by solving the continuity equation in the barrier region is proposed.     

蒙特卡罗模拟LED并联电路电流降额特性

利用蒙特卡罗方法对LED并联电路的电流降额特性进行了模拟,假设分档后的大功率白光LED的正向电压(VF)分布符合正态分布,研究了1×n(2≤n≤15)系列LED并联电路电流降额量(IP)的概率(P)分布。模拟结果表明,IP的概率分布函数偏离了正态分布,密度函数曲线最高值点的两侧不对称,左侧较右侧陡峭;随着LED并联数(n)的增加,概率密度函数沿IP增大的方向移动,并且越来越趋近于正态分布。当n一定时,IP随电路中出现LED承载电流超过其额定电流的概率增大而降低,降低的速度由快转慢;当P为0.01%～1%时,IP大约为20%～30%。当P一定时,IP随n的增加而增大;当n6时,IP的增大速度变缓。模拟结果可以推广到m×n阵列化互连大功率LED模组。     

Current fluctuations in stochastic lattice gases

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation theory for the space-time fluctuations of the empirical current which include the previous results. We then estimate the probability of a fluctuation of the average current over a large time interval. It turns out that recent results by Bodineau and Derrida [Phys. Rev. Lett. 92, 180601 (2004)]] in certain cases underestimate this probability due to the occurrence of dynamical phase transitions.     

The effects of tilt corrected residual aberration on the detection probability of single-photon propagation in a slant path turbulent atmosphere

Based on the assumption of a pulse laser beam with an initial Gaussian temporal shape and a collimated fundamental-model Gaussian beam, the Rytov approximation and Kolmogorov spectrum model for the index-of-refraction fluctuation of atmosphere, the effect of turbulence on the probability density, acquisition transmittance probability, transmittance probability density, acquisition probability of single-photon propagation in atmospheric communication channel with z-tilt and centroid-tilt aberration corrected are studied theoretically. The probability density, acquisition transmittance probability, transmittance probability density and acquisition probability models for single-photon propagation in uplink path and downlink path are derived. Our results shown that the detection probability and the acquisition transmittance probability of the single-photon are obvious increase, when the beams are propagation in the z-tilt corrected communication channel.     

GaAlAs-GaAs半导体激光器增益参数的研究

通过对半导体激光器发射光谱的计算可获得激光器的增益谱.本文研究了不同电流注入下激光器的增益特性;激光器的峰值增益系数Gmax在阈值电流以下随注入电流的增大而提高,也随结温的升高而下降.     

Eigenstates of Laser-Assisted Scattering in a Noninertial Frame

In a rotating noninertial frame, we investigate the eigenstates of the time-dependent problem for electronnucleus scattering assisted by a circularly polarized laser field. Numerical results of probability distribution, quantum potential, and current density are discussed. An approximate expression of scattering cross section for low laser frequency is given.     

Eigenstates of Laser-Assisted Scattering in a Noninertial Frame

In a rotating noninertial frame, we investigate the eigenstates of the time-dependent problem for electronnucleus scattering assisted by a circularly polarized laser field. Numerical results of probability distribution, quantum potential, and current density are discussed. An approximate expression of scattering cross section for low laser frequency is given.