在Jaynes－Cummings模型中压缩真空初态场位相演化特性

应用Ｐｅｇｇ－Ｂａｒｎｅｔｔ位相理论，研究了Ｊａｙｎｅｓ－Ｃｕｍｍｉｎｇｓ模型（Ｊ－Ｃ模型）中压缩真空初态场位相演化特性，具体计算了弱压缩条件下，场的位相几率分布函数及位相涨落，给出了在极坐标中位相几率分布演化曲线，讨论了原子与场相互作用对场的位相性质的影响。     

k（k〉2）光子Jaynes—Cummings模型中自发辐射场的位相演化特性

应用Ｐｅｇｇ－Ｂａｒｎｅｔ（ＰＢ）位相理论，研究了ｋ光子Ｊａｙｎｅｓ－Ｃｕｍｍｉｎｇｓ（Ｊ－Ｃ）模型中自发辐射场的位相演化特性，计算了辐射场的位相几率分布函数与位相涨落，给出了在极坐标中位相几率分布演化曲线。     

On Probability Domains II

We continue our studies of the foundation of probability theory using elementary category theory. We propose a classification scheme of probability domains in terms of cogenerators and their algebraic and topological properties and use the scheme to describe the transition from classical to fuzzy probability. We show that ?ukasiewicz tribes form a category of natural probability domains in which ??-fields of sets are ??minimal?? and measurable [0,1]-valued functions are ??maximal?? objects. The maximal objects form an epireflective subcategory in which both the classical and fuzzy probability can be modelled. This leads to a better understanding of the transition.     

Bell-type inequalities in classical probability theory

A review of the tomographic probability representation for qudit sates is presented. Properties of related stochastic matrices are considered. Tomograms of two qubits and three qubits are used to study the Bell-type inequalities. The Bell-type inequalities in the standard classical probability theory are discussed. Joint probability distributions of classical systems with several random variables and their properties in the case of factorized distribution functions are considered.     

压缩真空场与耦合双原子Raman相互作用过程中光场的相位演化特性

采用Pegg-Barnett相位理论，研究了压缩真空场与耦合双原子Raman相互作用过程中光场的相位演化特性.具体计算了场的相位概率分布函数及相位涨落，给出了在极坐标中概率分布变化曲线.讨论了原子与场相互作用、两原子间偶极-偶极相互作用以及原子初始状态对光场相位性质的影响. 关键词： 相位特性 压缩真空场 耦合双原子 Raman相互作用     

Entangled Qubit States and Linear Entropy in the Probability Representation of Quantum Mechanics

The superposition states of two qubits including entangled Bell states are considered in the probability representation of quantum mechanics. The superposition principle formulated in terms of the nonlinear addition rule of the state density matrices is formulated as a nonlinear addition rule of the probability distributions describing the qubit states. The generalization of the entanglement properties to the case of superposition of two-mode oscillator states is discussed using the probability representation of quantum states.     

The influence of the nanostructure geometry on the thermoelectric properties

We discuss the influence of nanostructure geometry on the thermoelectric properties in quantum ring consists of one QD in each arm, each QD connects with side QD. The calculations are based on the time-dependent Hamiltonian model, the steady state is considered to obtain an analytical expression for the transmission probability as a function of system energies. We employed the transmission probability to calculate the thermoelectric properties. We investigate thermoelectric properties through three configurations of this nanostructure. Figure of merit enhanced in configuration (II) when side QD connected to upper arm of quantum ring. The magnetic flux threads quantum ring. The effect of magnetic flux on the thermoelectric properties is examined.     

隧穿量子点分子模型与光场相互作用系统中光场的相位特性

应用Pegg-Barnett相位理论,研究了隧穿量子点分子模型与光场相互作用系统中光场的相位特性,着重分析了光场的相位概率分布及相位涨落,并讨论了平均光子数和失谐量以及时间对相位概率分布的影响．结果发现：光场相位概率分布在零附近的概率分布最大,且涨落最小,而其它范围内概率分布小且容易振荡,适当调节平均光子数和时间,能使相位概率分布由单峰结构向对称的三峰高斯分布转化,且能调节峰值的大小．     

Effect of driving laser intensity fluctuations on optical bistability of a system with large permanent-dipole molecules

The statistical properties of an optical bistable system consisting of two-level atoms with large permanent dipole moments contained in a Fabry-Perot cavity are investigated assuming the external laser intensity fluctuations to be the main source of noise. The probability transformation rule is applied to obtain the probability distribution for the transmitted intensity whereas the probability distribution for the incident intensity is assumed to be that of the partially coherent laser light. It turns out that in the optical bistability region two values of fluctuation parameters are possible for a given value of input intensity, which produces interesting hysteresis effects.     

Phase-space representation of quantum systems in the relative-state formulation

A phase-space representation of quantum systems within the framework of the relative-state formulation is proposed. To this end, relative-position and relative-momentum states are introduced and their properties are investigated in detail. Phase-space functions that represent a quantum state vector are constructed in terms of the relative-positive and relative-momentum states, and the quantum dynamics is investigated by using the phase-space functions. Furthermore, probability distributions in phase space are considered by means of the relativestate formulation, and it is shown that the phase-space probability distribution is closely related to the operational probability distribution. The marginal distribution, characteristic function, and operational uncertainty relation are also discussed.     

The influence of connectivity on the firing rate in a neuronal network with electrical and chemical synapses

We study the firing rate properties of a cellular automaton model for a neuronal network with chemical synapses. We propose a simple mechanism in which the nonlocal connections are included, through electrical and chemical synapses. In the latter case, we introduce a time delay which produces self-sustained activity. Nonlocal connections, or shortcuts, are randomly introduced according to a specified connection probability. There is a range of connection probabilities for which neuron firing occurs, as well as a critical probability for which the firing ceases in the absence of time delay. The critical probability for nonlocal shortcuts depends on the network size according to a power-law. We also compute the firing rate amplification factor by varying both the connection probability and the time delay for different network sizes.     

Single Photon Scattering in a Pair of Waveguides Coupled by a Whispering-Gallery Resonator Interacting with a Semiconductor Quantum Dot

The single photon scattering properties in a pair of waveguides coupled by a whispering-gallery resonator interacting with a semiconductor quantum dot are investigated theoretically.The two waveguides support four possible ports for an incident single photon.The quantum dot is considered a V-type system.The incident direction-dependent single photon scattering properties are studied and equal-output probability from the four ports for a single photon incident is discussed.The influences of backscattering between the two modes of the whispering-gallery resonator for incident direction-dependent single photon scattering properties are also presented.     

Tomographic entropy and cosmology

The probability representation of quantum mechanics including propagators and tomograms of quantum states of the universe and its application to quantum gravity and cosmology are reviewed. The minisuperspaces modeled by oscillator, free pointlike particle and repulsive oscillator are considered. The notion of tomographic entropy and its properties are used to find some inequalities for the tomographic probability determining the quantum state of the universe. The sense of the inequality as a lower bound for the entropy is clarified.     

Two-mode mazer injected with V-type three-level atoms

The properties of the two-mode mazer operating on V-type three-level atoms are studied. The effect of the oneatom pumping on the two modes of the cavity field in number-state is asymmetric, that is, the atom emits a photon into one mode with some probability and absorbs a photon from the other mode with some other probability. This effect makes the steady-state photon distribution and the steady-state photon statistics asymmetric for the two modes. The diagram of the probability currents for the photon distribution, given by the analysis of the master equation, reveals that there is no detailed balance solution for the master equation. The computations show that the photon statistics of one mode or both modes can be sub-Poissonian, that the two modes can have anticorrelation or correlation, that the photon statistics increases with the increase of thermal photons, and that the resonant position and strength of the photon statistics are influenced by the ratio of the two coupling strengths of the two modes. These properties are also discussed physically.     

在变值测量模拟中的条件概率统计分布

针对常见的两类量子交互干涉实验,Young 氏双缝干涉和超低强度长时间曝光量子交互结果显示出的明显波动统计分布特性,本文基于另一种经典概率测量模型Bayes统计依据的条件概率方法,提出条件概率变值测量模型,建立了测量模拟方法,给出了不同参量的测量公式,并对相关的重要条件进行描述.通过2个具体例子按每个函数形成四组16个直方图统计分布进行比较,对给定例子中的重要特性进行了分析.分析表明,在同步/异步、对称/反对称的作用下,条件概率测量模拟系统能针对左路、右路、双路粒子和双路波动交互作条件形成两类8种不同的统计分布.从不同的侧面显现了双路粒子同左/右路异步加算符信号之间的直接耦合关系,以及左/右路同步加算符信号与双路波动之间的干涉输出关系.在条件概率模型的条件下,单路/双路、粒子和波动的区别非常明晰,可以从中看到Feynman提炼的经典和量子统计之间的区别,统计判据直接从直方图分布中即可区分. 这类特性从基础层面显示了波/粒二重性的怪异特性,可以通过粒子性的模型完整描述.     

随机延迟概率对交通流的影响

考虑影响随机延迟概率的几种因素：当车速预期大于车距时，车辆处于减速状态，对前车状态变化的随机延迟反应较大，具有的延迟概率较大；当车速预 期 等于车距时，车辆处于平稳跟随行驶状态，具有的延迟概率较小；当车速预期小于车距时，车辆处于加速状态，其延迟概率最小. 计算机数值模拟得到的基本图不同于NaSch模型的基 本图，在基本图上出现阻塞的范围内存在两个不同的区域，分别对应于具有不同激波速度的交通阻塞. 同时，研究了交通阻塞到消散的滞后现象. 关键词： 交通流 元胞自动机模型 基本图 交通阻塞     

Radon transform and kinetic equations in the tomographic representation

Statistical properties of classical random processes are considered in the tomographic representation. The Radon integral transform is used to construct the tomographic form of the kinetic equations. The relationship between the probability density on the phase space for classical systems and the tomographic probability distribution is elucidated. Examples of simple kinetic equations like the Liouville equations for one and many particles are studied in detail.     

Ionization probability of the bound impurity states of two-dimensional electrons under strong magnetic and finite electric fields

The ionization probability of the bound impurity states in a semiconductor inversion layer under strong magnetic fields H is calculated as a function of temperature and electric field value E. The conditions for relatively large ionization probability are determined. The possibility of the bound state ionization must be taken into account for the interpretation of the inversion layer properties at the Shubnikov-De Haas conductivity minima.