Anisotropic Harmonic Oscillator in a Static Electromagnetic Field

A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schrödinger equation is solved analytically in most of the cases. The energy levels and wave functions are obtained explicitly. In some of the cases, the ground state obtained is not a minimum wave packet, though it is of the Gaussian type. Coherent and squeezed states and their time evolution are discussed in detail.     

Dynamics of a charged test particle in a hard rod fluid

The motion of a charged hard rod, accelerated by a constant and uniform external field, in a fluid of mechanically identical neutral particles is studied. The system, initially at rest, is excited through collisions with the accelerated particle. A class of initial configurations is found for which recollisions between the charged rod and the excitation caused by it (a moving particle) never occur. The evolution of the velocity distribution of the test particle is analyzed in this case. The possibility of obtaining from microscopic dynamics a kinetic equation is discussed. The dependence of the current on the external field is shown to agree with that predicted by the Boltzmann equation.     

Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schrödinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schrödinger equation and some special and limiting cases are outlined.     

基底性质对二维层状电子气感应电场的影响

采用线性化量子流体动力学模型,研究了载能粒子与二维层状电子气相互作用时的集体静电激发现象。在适当的边界条件下推导出感应电势,入射粒子所受的阻止力和侧向力的一般表达式,讨论了存在绝缘基底情况下基底介电常数对感应电势、阻止力及侧向力的影响。结果表明:当入射粒子速度较小时,基底的极化电场较弱,其介电常数的变化对感应电场几乎无影响,而当速度较高时因极化电场较强而影响很大;入射粒子距离与基底相连的电子气平面越近,基底介电常数对各物理量的影响越大。     

带电粒子在相互垂直的匀强电场和磁场中的运动轨迹

推导出带电粒子在相互垂直的匀强电场和磁场中普遍情况下的运动方程,给出了几种典型情况下的轨迹,并对轨迹的形状和性质,结点的出现进行了讨论.     

正弦平方势与小振幅近似下的弯晶沟道辐射

在理想情况下和经典力学框架内,引入正弦平方势,把粒子在弯晶中的运动方程化为具有外力矩的摆方程。并对系统的相平面特征进行了数值分析。在小振幅近似下,把粒子运动方程化为具有硬特性的弹簧-振子系统,用Jacobian椭圆函数和椭圆积分解析地给出系统的解和粒子运动周期。讨论了弯晶沟道辐射频率、无量纲偏转角和辐射谱的一般特征。指出利用沟道辐射作为激光的可能性。以正电子在碳单晶中沟道辐射为例进行了具体计算,得到了与其他工作基本一致的结果。     

复合场中的滚轮线

带电质点在正交的匀强电场(重力场)和匀强磁场中运动,轨迹为滚轮线.处理滚轮线问题的关键是构造匀速直线运动以平衡电场力(重力),从而将带电质点的运动分解为匀速直线运动和匀速圆周运动,简化问题的处理过程.     

Electromagnetic scattering of charged particles in a strong wind-blown sand electric field

Some field experimental results have shown that the moving sands or dust aerosols in nature are usually electrified,and those charged particles also produce a strong electric field in air, which is named as wind-blown sand electric field.Some scholars have pointed out that the net charge on the particle significantly enhances its electromagnetic(EM) extinction properties, but up to now, there is no conclusive research on the effect of the environmental electric field. Based on the extended Mie theory, the effect of the electric field in a sandstorm on the EM attenuation properties of the charged larger dust particle is studied. The numerical results indicate that the environmental electric field also has a great influence on the particle's optical properties, and the stronger the electric field, the bigger the effect. In addition, the charged angle, the charge density, and the particle radius all have a specific impact on the charged particle's optical properties.     

Evolution of Arbitrary States under Fock-Darwin Hamiltonian and a Time-Dependent Electric Field

The method of path integral is employed to calculate the time evolution of the eigenstates of a charged particle under the Fock-Darwin(FD) Hamiltonian subjected to a time-dependent electric field in the plane of the system.An exact analytical expression is established for the evolution of the eigenstates.This result then provides a general solution to the time-dependent Schro¨dinger equation.     

Time-dependent formulation of the linear unitary transformation and the time evolution of general time-dependent quadratic Hamiltonian systems

A time-dependent closed-form formulation of the linear unitary transformation for harmonic-oscillator annihilation and creation operators is presented in the Schrödinger picture using the Lie algebraic approach. The time evolution of the quantum mechanical system described by a general time-dependent quadratic Hamiltonian is investigated by combining this formulation with the time evolution equation of the system. The analytic expressions of the evolution operator and propagator are found. The motion of a charged particle with variable mass in the time-dependent electric field is considered as an illustrative example of the formalism. The exact time evolution wave function starting from a Gaussian wave packet and the operator expectation values with respect to the complicated evolution wave function are obtained readily.     

Some problems in the classical theory of radiation

The article considers the problem of the complete radiation of the energy of a charged particle moving in constant and homogeneous electric and magnetic fields and in the field of a plane wave. Exact formulas are obtained for these cases. The problem is al so considered of the instantaneous radiation of an arbitrary moving charge. The problems are considered according to classical theory.     

Asymptotic Behavior of the Quantum Harmonic Oscillator Driven by a Random Time-Dependent Electric Field

This paper investigates the evolution of the state vector of a charged quantum particle in a harmonic oscillator driven by a time-dependent electric field. The external field randomly oscillates and its amplitude is small but it acts long enough so that we can solve the problem in the asymptotic framework corresponding to a field amplitude which tends to zero and a field duration which tends to infinity. We describe the effective evolution equation of the state vector, which reads as a stochastic partial differential equation. We explicitly describe the transition probabilities, which are characterized by a polynomial decay of the probabilities corresponding to the low-energy eigenstates, and give the exact statistical distribution of the energy of the particle.     

Anisotropic Harmonic Oscillator in a Static Electromagnetic Field

A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneousstatic electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schrodingerequation is solved analytically in most of the cases. The energy levels and wave functions are obtained explicitly. Insome of the cases, the ground state obtained is not a minimum wave packet, though it is of the Gaussian type. Coherentand squeezed states and their time evolution axe discussed in detail.     

Relativistic charged particles in the field of an electromagnetic plane wave in a medium

Solutions of the Klein-Gordon and Dirac equation for a charged particle in the field of an electromagnetic plane wave in a medium with a constant refractive index n are discussed. Generally, for n² < 1, spontaneous pair creation from the vacuum, and for n² > 1, energy bands are observed. The interplay of Compton and Cherenkov scattering is discussed. Some doubts are formulated as to the physical relevance of calculating pair creation in a homogeneous electric field as it is usually done.     

Electric dipole moments of charged particles

The existence of an electric dipole moment (edm) on a fundamental atomic particle would imply violation of both parity and time-reversal invariance. An edm on a neutral particle is detectable through its interaction with an applied electric field. The search for edms on charged particles such as the nucleus or the electron is made difficult by their acceleration in an electric field; conversely, a charged particle in equilibrium must be shielded from the field and the edm interaction will then vanish. A number of ingenious ways around this shielding theorem are discussed, as are the use of polar molecules to amplify the residual edm interactions. A range of atomic and molecular beam and optical pumping experiments are described and the results tabulated. The implications for particle theories beyond the standard model are briefly summarized.     

Radiation of de-excited electrons at large times in a strong electromagnetic plane wave

The late time asymptotics of the physical solutions to the Lorentz–Dirac equation in the electromagnetic external fields of simple configurations–the constant homogeneous field, the linearly polarized plane wave (in particular, the constant uniform crossed field), and the circularly polarized plane wave–are found. The solutions to the Landau–Lifshitz equation for the external electromagnetic fields admitting a two-parametric symmetry group, which include as a particular case the above mentioned field configurations, are obtained. Some general properties of the total radiation power of a charged particle are established. In particular, for a circularly polarized wave and constant uniform crossed fields, the total radiation power in the asymptotic regime is independent of the charge and the external field strength, when expressed in terms of the proper-time, and equals a half the rest energy of a charged particle divided by its proper-time. The spectral densities of the radiation power formed on the late time asymptotics are derived for a charged particle moving in the external electromagnetic fields of the simple configurations pointed above. This provides a simple method to verify experimentally that the charged particle has reached the asymptotic regime.     

负径向电场对荷电粒子运动的影响及其数值模拟

从负径向电场产生的电漂移改变荷电粒子运动的极向运动速度着手,推导出在负径向电场存在时安全因子的表达式,分析了安全因子对荷电粒子漂移位移和运动轨迹的影响。建立了在负径向电场条件下,荷电粒子在梯度磁场和曲率磁场中运动数学模型。通过数值模拟,获得了通行粒子、香蕉粒子的漂移位移和运动轨迹所呈现出的新特点和规律:负径向电场改变了荷电粒子的最大漂移位移。当荷电粒子的极向运动速度增加时,最大漂移位移减小,反之增大;改变了荷电粒子的运动轨迹,通行粒子的轨亦可能变为香蕉粒子的轨迹,香蕉粒子的轨迹可能变为通行粒子的轨迹,当电场达到足够的强度时,均成为在极向上顺时针运动的通行粒子轨迹。     

正电子面沟道辐射的非线性特征

经典物理学指出,在电磁场中作加速运动的带电粒子将不断向外辐射能量.在晶体沟道中运动的带电粒子也不例外,晶格场可以使带电粒子的辐射能量达到很高.对于10MeV的正电子,辐射能量可达keV量级.粒子在沟道中的运动行为决定于粒子晶体的相互作用势,常用的相互作用势有Lindhard势、Moliere势和正弦平方势.由于粒子在沟道中的运动行为十分类似于震荡器中运动的自由电子,可望把沟道辐射改造为Χ射线激光或γ射线激光.从Lindhard势出发,将其展开到四次项,在经典力学框架内,粒子的运动方程可以化为含立方项的二阶非线性微分方程,并利用Jacobian椭圆函数和第一类全椭圆积分解析地表示了系统的解和粒子运动周期,导出了正电子面沟道辐射的瞬时辐射强度、平均辐射强度和最大辐射频率,指出了利用沟道辐射作为γ激光的可能性.     

带电粒子在正交电场和磁场中轨迹的形成及曲率半径

本文讨论了带电粒子在正交的电场和磁场中于不同条件下的旋轮线轨迹,并讨论了这些不同形状的旋轮线是怎样由圆轮的纯滚动形成的,使带电粒子的运动过程更加直观,并且运用物理方法导出了旋轮线曲率半径的普遍公式.