An Alternative Approach to the Classical Dynamics of an Extended Charged Particle

In this paper the analysis of the classical dynamics of a charged particle is carried out without considering that the electromagnetic field necessarily goes to zero at infinity. A quite general non-linear equation of motion is obtained for an extended charged particle valid for any distribution of charge in the particle and for an electromagnetic field satisfying any boundary conditions. Some common approximations are analyzed with detail to determine how the usual difficulties arise.     

Radiation Reaction of a Nonrelativistic Quantum Charged Particle

An alternative approach to analyze the nonrelativistic quantum dynamics of a rigid and extended charged particle taking into account the radiation reaction is discussed with detail. Interpretation of the field operators as annihilation and creation ones, theory of perturbations and renormalization are not used. The analysis is carried out in the Heisenberg picture with the electromagnetic field expanded in a complete orthogonal basis set of functions which allows the electromagnetic field to satisfy arbitrary boundary conditions. The corresponding coefficients are the field operators which satisfy the usual commutation relations. A nonlinear equation of motion for the charged particle is obtained. A careful consideration of the quantum effects allows the derivation of a linear equation of motion which is free of both runaway solutions and preacceleration, even for a point charge. Also, the electromagnetic mass, which is defined as the coefficient of the acceleration operator, vanishes for a point particle. However, this does not mean that the results are free of ambiguities which are exhibited and discussed.     

一般含时线性势的量子解及有关问题

对于一般形式的含时线性势, 通过假设波函数形式的方法得到了Schr?dinger方程的精确和完备解. 同时指出, 用两个波函数φ(t)〉和ψ(t)〉定义的坐标和动量的矩阵元〈φ(t)xψ(t)〉和〈φ(t)pψ(t)〉满足经典形式的运动方程. 按照量子力学的系综理论, 这样的经典形式的运动方程实际上是流体方程. 进一步研究发现, 对于任意形式的线性系统有类似的结论. 关键词： 线性势 Schr?dinger方程 Heisenberg对应原理 经典运动方程     

A Physical Deduction of an Equivalent Landau–Lifshitz Equation of Motion in Classical Electrodynamics. A New Expression for the Large Distance Radiation Rate of Energy

A new scheme is proposed in order to deduce an equation of motion for a spinless charged point particle leading to an equivalent Landau–Lifshitz equation of motion. Consequently Larmor’s formula must be substituted by a new expression for the large distance radiation rate of energy. A constraint appears on the applicability of the Maxwell electromagnetic tensor. The particular case of a sudden force is analyzed in order to show the physical results predicted by the new model. A geometrical rearrangement of the energy explains the balance.     

A Two-Surface Problem of the Electron Flow in a Semiconductor on the Basis of Kinetic Theory

A steady flow of electrons in a semiconductor between two parallel plane Ohmic contacts is studied on the basis of the semiconductor Boltzmann equation, assuming a relaxation-time collision term, and the Poisson equation for the electrostatic potential. A systematic asymptotic analysis of the Boltzmann–Poisson system for small Knudsen numbers (scaled mean free paths) is carried out in the case where the Debye length is of the same order as the distance between the contacts and where the applied potential is of the same order as the thermal potential. A system of drift-diffusion-type equations and their boundary conditions is obtained up to second order in the Knudsen number. A numerical comparison is made between the obtained system and the original Boltzmann–Poisson system.     

Analytical Solutions of a Model for Brownian Motion in the Double Well Potential

In this paper, the analytical solutions of Schr¨odinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential for Brownian motion is always used to obtain the solutions of Fokker–Planck equation known as the Klein–Kramers equation, which is suitable for separation and additive Hamiltonians. In essence, we could study the random motion of Brownian particles by solving Schr¨odinger equation. The analytical results obtained from the two different methods agree with each other well. The double well potential is affected by two parameters, which are analyzed and discussed in details with the aid of graphical illustrations. According to the final results, the shapes of the double well potential have significant influence on the probability density function.     

A Practical Algorithm for Determining the Optimal Pseudo-Boundary in the Method of Fundamental Solutions

One of the main difficulties in the application of the method of fundamental solutions (MFS) is the determination of the position of the pseudo-boundary on which are placed the singularities in terms of which the approximation is expressed. In this work, we propose a simple practical algorithm for determining an estimate of the pseudo-boundary which yields the most accurate MFS approximation when the method is applied to certain boundary value problems. Several numerical examples are provided.     

A convergent nonequilibrium statistical mechanical theory for dense gases. II. Transport coefficients to first order in the density

Using the two-body distribution function found earlier by the authors with the aid of new boundary conditions, the kinetic equation and the transport coefficients are obtained to zeroth and first order in the density. To zeroth order we recover the Boltzmann kinetic equation. To first order the resulting expressions differ from the ones obtained by Choh and Uhlenbeck, due to effects of the medium.3 Reference 2 will be referred to as I. Here we use the same notation as in I.     

A high-order numerical method for the nonlinear Helmholtz equation in multidimensional layered media

We present a novel computational methodology for solving the scalar nonlinear Helmholtz equation (NLH) that governs the propagation of laser light in Kerr dielectrics.