Quasiprobability and Probability Distributions for Spin-1/2 States

We develop a Radon-like transformation, in which P quasiprobability distribution for spin-1/2 states is written in terms of the tomographic probability distribution w.     

Observables,Evolution Equation,and Stationary States Equation in the Joint Probability Representation of Quantum Mechanics

Symplectic and optical joint probability representations of quantum mechanics are considered, in which the functions describing the states are the probability distributions with all random arguments (except the argument of time). The general formalism of quantizers and dequantizers determining the star product quantization scheme in these representations is given. Taking the Gaussian functions as the distributions of the tomographic parameters the correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators in the form of singular and regular generalized functions are derived. Evolution equations and stationary states equations for symplectic and optical joint probability distributions are obtained.     

Eletroweak Form Factors in the Light-Front for Spin-1 Particles

The contribution of the light-front valence wave function to the electromagnetic current of spin-1 composite particles is not enough to warranty the proper transformation of the current under rotations. The naive derivation of the plus component of the current in the Drell–Yan–West frame within an analytical and covariant model of the vertex leads to the violation of the rotational symmetry. Computing the form-factors in a quasi Drell–Yan–West frame q ⁺ → 0, we were able to separate out in an analytical form the contributions from Z-diagrams or zero modes using the instant-form cartesian polarization basis.     

The State Space of a Pair of Spin-1/2 Particles

The state space of a quantum mechanical systemconsisting of more than one particle exhibits someunusual features giving rise to interesting phenomena,such as the Einstein–Rosen–Podolsky paradox.In order to get a feel for the structure of such a statespace, it is useful to study the spin component of apair of spin-1/2 particles, whose associated state spaceis clearly the simplest example occurring within the context of quantum mechanical systems ofmore than one particle. In a series of papers R.Horodecki et al. did just that and they found somebeautiful results, which are certainly of interest tothe mathematical physicist. In the present note, ina different context and using somewhat different methodsof proof, we rederive some of the results obtained byHorodecki. Furthermore, using these methods we are able to prove some additional resultswhich to our knowledge have never beenpublished.     

Relativistic Quantum Correlations Between Spin-1/2 Particles

It is shown that a fully relativistic formulation of spin measurements and correlations does not add any new feature to the standard analysis of Bell and the deduction of his inequality. It follows, therefore, that the motion of reference frames does not affect the correlations between spatially separated particles.     

AIM Solutions to the DKP Equation for Spin-1 Particles in the Presence of Kratzer Potential in (2+1) Dimensions

The relativistic Duffin–Kemmer–Petiau equation for spin-1 particles in the presence of the Kratzer potential is studied analytically within the framework of the asymptotic iteration method. The exact energy eigenvalues and corresponding eigenfunctions of spin-1 particles are obtained for arbitrary quantum states by solving the Duffin–Kemmer–Petiau equation with Kratzer potential.     

On a Kinetic Equation for Coalescing Particles

Existence of global weak solutions to a spatially inhomogeneous kinetic model for coalescing particles is proved, each particle being identified by its mass, momentum and position. The large time convergence to zero is also shown. The cornestone of our analysis is that, for any nonnegative and convex function, the associated Orlicz norm is a Liapunov functional. Existence and asymptotic behaviour then rely on weak and strong compactness methods in L¹ in the spirit of the DiPerna-Lions theory for the Boltzmann equation.     

Probability Collectives for Unstable Particles

Unstable particles, together with their stable decay products, constitute probability collectives that are defined as Hilbert spaces with dimension higher than one, nondecomposable in a particle basis. Their structure is considered in the framework of Birkhoff-von Neumann's Hilbert subspace lattices. Bases with particle states are related to bases with a diagonal scalar product by a Hilbert-bein involving the characteristic decay parameters (in some analogy to the n-bein structures of metrical manifolds). Probability predictions as expectation values, involving unstable particles, have to take into account all members of the higher dimensional collective. For example, the unitarity structure of the S-matrix for an unstable particle collective can be established by a transformation with its Hilbert-bein.     

微粒形体特征概率分布函数的光散射频谱分析法

针对微粒(包括生物微粒)光散射测量中微粒形体对测量结果的影响以及形体分布不能实时测量的问题,本文根据光散射测量原理,从微粒群的统计性出发,对散射脉冲的脉宽、脉峰分布及其与微粒大小和形体分布物理动态特征的相互关系进行了系统的分析,得到了微粒形体、微粒大小分布与其散射谱分布的特征关系,提出了等值概率面积确定法则,并据此建立了一种实时由散射谱一体分析获取微粒形体特征分布的方法,得到了较好的实验验证,由此可有效地修正因微粒形体变化而对测量精度的影响,从而为粒度分析仪以及以光散射原理为测量理论的流式细胞仪技术的提升提供了有力的基础。     

Nonlinear Langevin Equation for a System of Coulomb Particles

The nonlinear Langevin equation for a system of Coulomb particles with random processes, which are functionals of the velocity distribution function of such particles, has been derived and analyzed. It is shown by direct numerical solutions that this equation correctly describes the collisional relaxation of such a system even in the case of anomalous deviation of the initial velocity distribution of particles from the equilibrium distribution. The equation can be conveniently used in the Monte Carlo methods and in “particle-in-cell” methods.     

任意形体微粒分布的概率表述及其测量方法

对任意形体的三维微粒，引入了等相位二维散射截面的概念，建立了半椭圆概率组合模型，提出了形体特征参数η、影响因子T（η）与其形体概率分布函数P^η（η）的概念，以特征分布函数P（α，η）取代了球形粒度概率分布函数P^s(a)，在洛伦兹－米（Lorenz-Mie)散射理论的基础上，建立了P（α，η）的数学反演方程和实验测量方法。理论结果经非球形煤粉微粒的实验验证，效果较好。     

A Nonmonotonic Theory of Probability for Spin- $$\textstyle{1 \over 2}$$ Systems

Kolmogorov's theory of probability is monotonic, meaning that the probability of A is less than or equal to the probability of B whenever A entails B. A nonmonotonic theory of probability is obtained, if the greatest lower bound for probabilities is set at −1 instead of 0, the value fixed by Kolmogorov's positivity axiom. The new theory retains Kolmogorov's other axioms, and many important theorems still hold. It also has substantial applicability: it can accommodate probabilities for spin- systems while preserving Boolean operations. That is to say, negative probabilities are here provided with a homely setting in the quantum domain. PACS : 03.65.-w, 03.65.Ta, 34.80.Nz.     

Spin-1 particle in a homogeneous magnetic field

The Corben-Schwinger theory gives imaginary values of the energy, forS ₃ ² =1 states, in very intensive magnetic fields. The theory proposed by the author, which is most satisfactory in the nonrelativistic approximation, does not have this defect forS ₃ ² =1 states, but it appears forS ₃ ² =0 states.     

Fidelity for States of Two Spin- $\frac{1}{2}$ Particles in Moving Frames

Fidelity for the spin part of states of two spin- particles is investigated from the viewpoint of moving observers. Using a numerical approach, the behavior of the fidelity in terms of the boost parameter is described for different amounts of spin entanglement and momentum entanglement. It is shown that for the spin entangled states the fidelity decreases less than that of the case of spin product states and there are special cases for which the fidelity remains perfect regardless of moving observers’ velocity. Generally, in the limit of boosts with speeds close to the speed of light, the fidelity saturates, i.e., it reaches to a constant value that depends on the amount of momentum entanglement and the width of the momentum distribution function.     

Quantum Correlations of Two Relativistic Spin-12 Particles Under Noisy Channels

We study the quantum correlation dynamics of bipartite spin-\(\frac {1}{2}\) density matrices for two particles under Wigner rotations induced by Lorentz transformations which is transmitted through noisy channels. We compare quantum entanglement, geometric discord(GD), and quantum discord (QD) for bipartite relativistic spin-\(\frac {1}{2}\) states under noisy channels. We find out QD and GD tend to death asymptotically but a sudden change in the decay rate of the entanglement occurs under noisy channels. Also, bipartite relativistic spin density matrices are considered as a quantum channel for teleportation one-qubit state under the influence of depolarizing noise and compare fidelity for various velocities of observers.     

介质中含孤立发光中心的纳米粒子的辐射寿命概率分布

含发光中心的纳米粒子在介质中随机分布,造成局域介质相对折射率的随机分布,导致了纳米粒子辐射寿命的涨落.分析纳米粒子数量在线度为发射光波长量级的体积内的概率密度,由此得出局域介质相对折射率的概率密度.通过纳米粒子辐射寿命对折射率的依赖关系,得到纳米粒子辐射寿命概率密度的解析表达.在此基础上,分析了Meltzer等人的实验中,含Eu³⁺离子的Y₂O₃粒子在甲醇溶液中辐射寿命的相对偏移量的涨落,并得出辐射寿命的不确定度(均方差)与纳米粒子体积、体积密度等物理量的关系.     

Exciton-Dependent Pre-formation Probability of Composite Particles

In Iwamoto-Harada model the whole phase space is full of fermions. When the momentum distributions of the exciton states are taken into account, the pre-formation probability of light composite particles could be improved, and the exciton state-dependent pre-formation probability has been proposed. The calculated results indicate that the consideration of the momentum distribution enhances the pre-formation probability of [1, m] configuration, and suppresses that of [ι 〉 1, m] configurations seriously.