Interference of probabilities and number field structure of quantum models

We study the probabilistic consequences of the choice of the basic number field in the quantum formalism. We demonstrate that by choosing a number field for a linear space representation of quantum model it is possible to describe various interference phenomena. We analyse interference of probabilistic alternatives induced by real, complex, hyperbolic (Clifford) and p‐adic representations.     

Matrix perturbation theory for driven three‐level systems with damping

We investigate the dynamics of the Λ system driven by two resonant laser fields in presence of dissipation for coupling strengths where the rotating‐wave approximation starts to break down. This regime is characterised by Rabi frequencies being approximately equal or smaller than the field frequencies. A systematic procedure to obtain an expansion for the solution of the Bloch evolution equations of the system is presented. The lowest contribution results to be the well‐known rotating‐wave approximation. The method is based on a semi‐classical treatment of the problem, and its predictions are interpreted fully quantum mechanically. The theory is illustrated by a detailed study of the disappearance of coherent population trapping as the intensities of the fields increase.     

FJZ-250型高速分幅相机时间测量不确定度分析

FJZ-250型高速转镜分幅相机因转镜速度的不可重复性，光机结构的构造原理和控制系统各路高压触发时间的漂移，导致了时间测量的不确定度。为此，须对相机测量数据进行校正。阐述了校正方法、提供了逐幅校正位置误差的修正系数。若以预置转速对应的名义周期值去处理测量结果，则相机的时间测量合成小确定度将达1％，对名义周期值和名义幅间间隔时间值进行修正后，则可降至0.3％。     

量子算法的NMR实现方法

量子计算机是一种以量子耦合方式进行信息处理的装置[1 ] 。原则上 ,它能利用量子相干干涉方法以比传统计算机更快的速度进行诸如大数的因式分解、未排序数据库中的数据搜索等工作[2 ] 。建造大型量子计算机的主要困难是噪音、去耦和制造工艺。一方面 ,虽然离子陷阱和光学腔实验方法大有希望 ,但这些方法都还没有成功实现过量子计算。另一方面 ,因为隔离于自然环境 ,核自旋可以成为很好的“量子比特” ,可能以非传统方式使用核磁共振 (NMR)技术实现量子计算。本文介绍一种用NMR方法实现量子计算的方法 ,该方法能够用比传统方法少的步骤解决一个纯数学问题。基于该方法的简单量子计算机使用比传统计算机使用更少的函数“调用”判断一未知函数的类别。     

Virtual logarithms

The modification of the number field sieve which Joux and Lercier recently used to compute logarithms in a prime field of a record 120 decimal digits makes use of the notion of a virtual logarithm of a prime ideal in a number ring. We provide necessary and sufficient conditions for their method to succeed and give an explicit formula for the virtual logarithm of an ideal.     

相对论平均场理论中各种有效相互作用对中子星性质的影响

基于相对论平均场理论，研究了各种相互作用参数组(NL1、NL3、NLSH、TM1和GL-97)对中子星物质的性质和中子星整体结构的影响．发现参数组NL1、NL3和NLSH所给出的中子星内部的介子场强度、物质的组成比例、物态方程和中子星的整体特点基本相同，但与TM1和GL-97之间有较大的差别．相对于其他参数组，GL-97给出的介子场强度最弱，中子星的相对数密度最大，物态方程也最软，同时采用GL-97参数组计算的中子星的最大质量也最小．     

Transport of Neutrally Buoyant and Dense Variably Sized Colloids in a Two-Dimensional Fracture with Anisotropic Aperture

The transport of monodisperse as well as polydisperse colloid suspensions in a two-dimensional, water saturated fracture with spatially variable and anisotropic aperture is investigated with a particle tracking model. Both neutrally buoyant and dense colloid suspensions are considered. Although flow and transport in fractured subsurface formations have been studied extensively by numerous investigators, the transport of dense, polydisperse colloid suspensions in a fracture with spatially variable and anisotropic aperture has not been previously explored. Simulated snapshots and breakthrough curves of ensemble averages of several realizations of a log-normally distributed aperture field show that polydisperse colloids exhibit greater spreading than monodisperse colloids, and dense colloids show greater retardation than neutrally buoyant colloids. Moreover, it is demonstrated that aperture anisotropy oriented along the flow direction substantially increases colloid spreading; whereas, aperture anisotropy oriented transverse to the flow direction retards colloid movement.     

Group Representation of Relativistic Quantum Crystal Optics

A group representation of radiation propagation in an anisotropic medium is developed. The system of wave equations for electromagnetic potentials, obtained from the Maxwell equations with account for the constitutive equations, has been factorized. It is shown that the linear differential operator of the factorized system is orthogonal in transparent crystals and unitary in gyrotropic ones and is represented through the momentum operator. On the basis of the commutation relations for the components of this operator, the eigenvalue problem has been solved and the expression for the change in the radiant energy in the crystal in the form of spherical waves has been obtained. The dependences of the ray and phase velocities and the polarization vectors of waves on the birefringence anisotropy and gyrotropy as well as on the angular momentum, displacement current, and bound charge determining them have been analyzed. It has been established that in the general case of gyrotropic crystals where the nonreciprocity phenomenon takes place and in magnetoelectrics Maxwell equations are represented in a form similar to the Dirac equations and the electromagnetic radiation is correctly described by means of bispinors and is quantized as fermions.     

Neutrino propagation in a weakly magnetized medium

Neutrino-photon processes, forbidden in vacuum, can take place in the presence of a thermal medium and/or an external electro-magnetic field, mediated by the corresponding charged leptons (real or virtual). Such interactions affect the propagation of neutrinos through a magnetized plasma. We investigate the neutrino-photon absorptive processes, at the one-loop level, for massless neutrinos in a weakly magnetized plasma. We find that there is no correction to the absorptive part of the axial-vector-vector amplitude due to the presence of a magnetic field, to the linear order in the field strength.     

On computation of the greatest common divisor of several polynomials over a finite field

We propose a probabilistic algorithm to reduce computing the greatest common divisor of m polynomials over a finite field (which requires computing m−1 pairwise greatest common divisors) to computing the greatest common divisor of two polynomials over the same field.