Reparametrization of the Relativistic Infinitely Extended Charged Particle Action

In this letter, relativistic infinitely extended particles formulated. Correct form of action with possibility of reparametrization obtained and effect of electric field considered. It may be one of the first step to re-introduce theory of every things given by Nakano and Hessaby many years ago.     

On the Long Time Behavior of a Particle in an Infinitely Extended System in One Dimension

We study the long time behavior of a non-equilibrium infinite particle system in one dimension. First, we show that the velocity of a particle increases at most linearly in time. Then we discuss at a heuristic level the displacement of a particle when the mutual interaction is singular. Finally we study the motion of a fast particle interacting with a background of slow particles and we prove that the velocity of the fast particle remains almost unchanged for a long time (at least proportional to the velocity itself).     

On the Long Time Behavior of Infinitely Extended Systems of Particles Interacting via Kac Potentials

We analyze the long time behavior of an infinitely extended system of particles in one dimension, evolving according to the Newton laws and interacting via a non-negative superstable Kac potential (x)=(x), (0, 1]. We first prove that the velocity of a particle grows at most linearly in time, with rate of order . We next study the motion of a fast particle interacting with a background of slow particles, and we prove that its velocity remains almost unchanged for a very long time (at least proportional to ^–1 times the velocity itself). Finally we shortly discuss the so called Vlasov limit, when time and space are scaled by a factor .     

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.     

Motion of a Charged Particle in an Arbitrary Time-Dependent Electric Field with Alternating Intersite Interactions

The motion of a charged particle on a linear chain under the action of an electric field with alternating intersi te interactions is investigated. Exact solutions for the Wannier state amplitudes, the propagators and the mean square displacement are obtained for the general case of an arbitrary time-dependent electric field, of which a dc+ac electric field is only a special one. The dynamic localization condition is given for this special case. This condition would make the observation of dynamic localization effect possible.     

Gravitational Waves Interacting with a Spinning Charged Particle in the Presence of a Uniform Magnetic Field

The equations which determine the response of a spinning charged particle moving in a uniform magnetic field to an incident gravitational wave are derived in the linearized approximation to general relativity. We verify that 1) the components of the 4-momentum, 4-velocity and the components of the spinning tensor, both electric and magnetic moments, exhibit resonances and 2) the co-existence of the uniform magnetic field and the GW are responsible for the resonances appearing in our equations. In the absence of the GW, the magnetic field and the components of the spin tensor decouple and the magnetic resonances disappear.     

Perturbations of the Motion of a Charged Particle in a Noisy Magnetic Field

We consider deterministic and stochastic perturbations of the motion of a charged particle in a noisy magnetic field. The noise in the magnetic field leads to the mixing on the energy surfaces and allows to apply averaging principle. We describe long-time energy evolution and its metastable states for a given initial energy and a time scale.     

带电粒子与静电波相互作用单粒子方程的严格解

研究了带电粒子与静电波之间的相互作用, 给出了带电粒子运动方程的严格解, 得出了粒子的速度的解析表达式, 同时推导出了带电粒子被静电波俘获的数学条件, 讨论了粒子与波能量交换的物理过程, 对现有等离子体物理的教材中相关的问题是一个补充. 本文结果对带电粒子加速器、微波管以及基础等离子体问题的研究有一定参考意义.     

带电粒子与静电波相互作用单粒子方程的严格解

研究了带电粒子与静电波之间的相互作用,给出了带电粒子运动方程的严格解,得出了粒子的速度的解析表达式,同时推导出了带电粒子被静电波俘获的数学条件,讨论了粒子与波能量交换的物理过程,对现有等离子体物理的教材中相关的问题是一个补充.本文结果对带电粒子加速器、微波管以及基础等离子体问题的研究有一定参考意义.     

Vacuum Fluctuations and Motion of a Charged Test Particle in a Cylindrical Spacetime

The effects of quantum electromagnetic fluctuations upon the motion of a test charged particle are examined in a cylindrical spacetime in which one spatial is compactified. The mean squared fluctuations in the velocity and position of the test particle are calculated. It is found that the random motion of the test particle will be anisotropic. The possible consequences for theories with extra compactified spatial dimensions are discussed.     

Speedy Motions of a Body Immersed in an Infinitely Extended Medium

We study the motion of a classical point body of mass M, moving under the action of a constant force of intensity E and immersed in a Vlasov fluid of free particles, interacting with the body via a bounded short range potential Ψ. We prove that if its initial velocity is large enough then the body escapes to infinity increasing its speed without any bound (runaway effect). Moreover, the body asymptotically reaches a uniformly accelerated motion with acceleration E/M. We then discuss at a heuristic level the case in which Ψ(r) diverges at short distances like gr ^−α , g,α>0, by showing that the runaway effect still occurs if α<2.     

Random Motion of a Charged Test Particle with a Constant Classical Velocity in a Spacetime with a Plane Boundary

We study the random motion of a charged test particle coupled to electromagnetic vacuum fluctuations near a perfectly reflecting plane boundary with a nonzero classical constant velocity in a direction parallel to the plane. We calculate the mean squared fluctuations in the velocity and position of the test particle taking into account both fluctuating electric and magnetic forces. Our results show that the influence of fluctuating magnetic fields is, in general, of the higher order than that caused by fluctuating electric fields and is thus negligible.     

Mixing Properties for Mechanical Motion¶of a Charged Particle in a Random Medium

We study a one-dimensional semi-infinite system of particles driven by a constant positive force F which acts only on the leftmost particle of mass M, called the heavy particle (the h.p.), and all other particles are mechanically identical and have the same mass m < M. Particles interact through elastic collisions. At initial time all neutral particles are at rest, and the initial measure is such that the interparticle distances ξ _i are i.i.d. r.v. Under conditions on the distribution of ξ which imply that the minimal velocity obtained by each neutral particle after the first interaction with the h.p. is bigger than the drift of an associated Markovian dynamics (in which each neutral particle is annihilated after the first collision) we prove that the dynamics has a strong cluster property, and as a consequence, we prove existence of the discrete time limit distribution for the system as seen from the first particle, a ψ-mixing property, a drift velocity, as well as the central limit theorem for the tracer particle. Received: 22 March 2000 / Accepted: 8 December 2000     

Random Motion of a Charged Test Particle with a Classical Constant Velocity in Vacuum in a Cylindrical Spacetime

We examine the random motion of a charged test particle with a nonzero classical velocity driven by quantum electromagnetic vacuum fluctuations in a cylindrical spacetime and calculate both the velocity and position dispersions of the test particle. It is found that the dispersions display different behaviour in different directions. These differences can be understood as a result of the topology of the configuration and initial physical conditions.     

Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas

We study a system consisting of a heavy quantum particle, called the tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density ${\to \infty}$ ). Our estimates allow us to interchange the thermodynamic with the mean-field limit.     

Chaotic Motion of a Charged Particle around a Weakly Magnetized Schwarzschild Black Hole Containing Cosmic String

We discuss the conditions where a charged particle that was originally revolving around a weakly magnetized black hole containing cosmic string in the innermost stable circular orbit will escape to infinity after it is kicked by another particle or photon. We find that the motion of the kicked particle is chaotic. The critical escape energy and velocity of the kicked charged particle with different initial radial velocities are obtained.     

Twist Property of Periodic Motion of an Atom Near a Charged Wire

We study the Lyapunov stability of periodic motion of an atom in the vicinity of an infinite straight wire with an oscillating uniform charge, which serves as a mechanism for trapping cold neutral atoms. It is proved by King and Leséniewski that the system has classical periodic motion for a certain range of parameters. In this Letter, we will prove, using the Birkhoff Normal Forms and Morse Twist Theorem, that such a periodic state is of twist type. As a result, besides the stability of the periodic state in the sense of Lyapunov, the system has infinitely many interesting bound states such as subharmonics and quasi-periodic states.