A Hamiltonian yielding damped motion in an homogeneous magnetic field: quantum treatment

In earlier work, a Hamiltonian describing the classical motion of a particle moving in two dimensions under the combined influence of a perpendicular magnetic field and of a damping force proportional to the particle velocity, was indicated. Here we derive the quantum propagator for the Hamiltonian in different representations, one corresponding to momentum space, the other to position, and the third to a natural choice of “velocity” variables. We call attention to the following noteworthy fact: the Hamiltonian contains three parameters which do not in any way influence the motion of the position of the particle. However, at the quantum level, the propagator, even in the position representation, depends in an intricate way on these classically irrelevant parameters. This creates considerable doubt as to the validity of such a quantization procedure, as the physical results predicted differ for various Hamiltonians, all of which describe the dissipative dynamics equally well.     

Brownian motion in a quantizing magnetic field

A model previously discussed by the author to study Brownian motion of charged carriers in a quantizing magnetic field is extended to include a Landau level-dependent friction parameter. A phase-space Fokker-Planck equation is used to derive a generalized diffusion equation describing spatial diffusion of the carriers, coupled with random jumps between adjacent Landau levels. This partial differential-difference equation is solved analytically. The longitudinal “global” diffusion coefficient is calculated and shown to be enhanced over the value in the extreme quantum limit.     

Hamiltonian structure of particle motion in an ideal helical wiggler with guide field

The ideal helical wiggler with guide field is shown to possess an integrable hamiltonian. Explicit generating functions are presented for the canonical transformation to action-angle variables.     

Determining pore sizes using an internal magnetic field

A concept is proposed to measure the pore size length scale by the internal magnetic field (B_i) in porous materials. The spatial distribution of the magnetic field inhomogeneity, a result of the magnetic susceptibility contrast between the porous material and the fluid, reflects the underlying pore geometry. Diffusion in B_i causes the initial decay of magnetization. At long times, the effect of B_i saturates when the diffusion length reaches a characteristic pore size. This method is independent of surface spin relaxation in determining pore sizes. Nuclear magnetic resonance experiments on packed glass beads and sedimentary rock samples will be presented.     

Brownian motion of a charged particle in a magnetic field

We develop and numerically illustrate an exact solution of the multivariate, stochastic, differential equations that govern the velocity and position of a charged particle in a plane normal to a uniform, stationary, magnetic field. The equations self-consistently incorporate the Lorentz force into an Ornstein-Uhlenbeck collision model. Properties of the solution in the infinite dissipation limit are explored and the spectral energy density function is found     

Hamiltonian for a symmetric-top molecule in an electric field

A method is presented by which one can systematically derive the types of terms, with regard to rotational as well as electric-field dependence and vibronic selection rules, that can occur in the effective Hamiltonian for a symmetric-top molecule placed in a homogeneous electric field. Rotation and molecular point groups somewhat modified from the ordinary ones are used for the derivation. The method is applied to the case of a C_3v molecule as an example, yielding a list of the operators occurring in the effective Hamiltonian with an electric-field dependence up to the second order.     

Radial motion of a solid spherical body in a magnetic field

The object of the present paper is to investigate the radial motion of a solid spherical body, assumed to be homogeneous, isotropic and elastic, in presence of a magnetic field in the azimuthal direction. The body is assumed to be in a state of initial stress which is hydrostatic in nature. This theory of radial motion of a solid spherical body in a magnetic field has been utilised to find the small radial motion of a solid Earth assumed to be homogeneous isotropic elastic sphere in presence of a magnetic field in the azimuthal direction. Considering the effect of gravity and the initial stress produced by slow process of creep due to extra masses over the surface of the Earth, the fundamental equations of motion are derived which are non-linear in character and are solved. The times of a desired radial displacement are calculated in presence of a magnetic field only and in presence of the same magnetic field, initial stress and gravitational field, which are compared and exhibited numerically.     

Electrically stimulated motion of dislocations in a constant magnetic field

This paper reports on the results of investigations into the dislocation mobility in n-Si single crystals (N _d =5×10²⁴ m^?3) upon simultaneous exposure to electric (j=3×10⁵ A/m²) and magnetic (B≤1 T) fields. It is found that the introduction of dislocations (≈10⁹ m^?2) into dislocation-free silicon doped with phosphorus leads to the appearance of the paramagnetic component of the magnetic susceptibility. The paramagnetic component increases with an increase in the dopant concentration. Similar transformations in silicon account for the formation of magnetically sensitive impurity stoppers that respond to external magnetic perturbations. An analysis of the behavior of dislocations in electric and magnetic fields has revealed a parabolic dependence of the dislocation path length on the magnetic induction B. The effective charges and mobilities of dislocations are numerically calculated from the results obtained. A model is proposed according to which the observed increase in the dislocation mobility is associated with the decrease in the retarding power of magnetically sensitive stoppers due to a local change in the magnetic characteristics of the material and the spin-dependent reactions stimulated by a magnetic field.     

The state of an atomic-molecular system near the stability threshold

The state of an atomic-molecular system near its stability threshold with regard to the detachment of one of the particles is studied. The decay of the system upon a decrease in the charge of a binding particle, as well upon an increasasymmetry of masses of like-charged particles, is considered. A special variational principle that allows one to directly calculate the threshold state of the system without repeatedly calculating its energy for different values of masses and charges of particles is used. With the motion of all particles fully taken into account, the threshold states of two-electron atoms with different nuclear charges and of atomic-molecular systems corresponding to the attachment of a positron of variable mass to a neutral atom are calculated. On the basis of calculation of quantum-mechanical expectation values of the kinetic energy of particles and the potential energy of their interaction, the rearrangement of the wave function upon passage of the system through the decay threshold is examined. The threshold characteristics of a purely adiabatic system containing infinitely heavy particles are considered separately.     

Oscillations of charged particles in an external magnetic field about steady motion

We develop a Hamiltonian formalism that can be used to study the particle dynamics near stable equilibria. The construction of an original canonical transformation allowed us to prove the conservation of the linear momentum P₃, which permitted the expansion of the Hamiltonian about a fixed point. The definition of the rotational variable h whose Poisson algebra properties played the essential role in the diagonalization of the quadratic Hamiltonian yielding two uncoupled oscillators with definite frequencies and amplitudes. It is through applying this variable near a fixed point that come to light Heisenberg's and Harmonic Oscillator equations of motion of the particles, leading thus the association of the fixed point trajectories with arbitrary trajectories in its immediate neighborhood. The present formalism succeeded to treat the problem of free-electron laser dynamics and may be applied to similar cases. Received 20 October 2001     

Electromagnetic field of a rotating magnetic dipole and electric-charge motion in this field

In this paper, we present the results of a study of the electromagnetic field in the near and intermediate zones of a magnetic dipole rotating in free space. Examples of solving the relativistic equations of the charged-particle motion in this field are given. The energy, which can be acquired by the particles during acceleration, is estimated.     

Stresses induced in polymer crystals by the atomic-molecular internal dynamics

The temperature dependences of the dynamic tensile stresses on the chemical bonds of the skeleton of chain molecules and the bonds between molecules in poly(ethylene) and polyamide 6 crystals are measured using X-ray diffraction and Raman spectroscopy in the temperature range 5–500 K. The relations of the dynamic stresses to the quantum characteristics of the vibrational dynamics of polymer molecules are derived. The contributions from the zero-point and thermal vibrations of molecules to the stresses are determined. It is revealed that the dynamic tensile stresses on the intermolecular bonds at the melting temperatures of the crystals approach the tensile strength of these bonds. Original Russian Text ? V.I. Vettegren, A.I. Slutsker, V.B. Kulik, 2009, published in Fizika Tverdogo Tela, 2009, Vol. 51, No. 1, pp. 198–205.     

Peculiarities of motion of a ferrofluid drop in a rotating magnetic field

The motion of a ferrofluid drop in a liquid nonmagnetic medium under the action of a rotating magnetic field is analyzed experimentally. A deviation of the falling drop from the vertical direction in the fields exceeding a certain critical value is detected. An extremum of the dependence of the deviation of the drop on the frequency of the rotating field is also observed. The results are analyzed theoretically and the algorithm of the numerical solution of the problem is proposed.     

Lagrangian equations of motion for a massive conductor in a magnetic field

The motion of a nonferromagnetic massive conductor is considered in a quasi-inhomogeneous, varying magnetic field. It is shown that the equations of motion can be written in Lagrangian form.SUNTs. M. V. Lomonosov Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 63–69, July, 1994.     

On the motion of a charged particle in a helical magnetic field

The rectilinear motion of a charged particle in a helical magnetic field is analyzed. Averaging methods are used as a device to study the equations of motion. The averaged system is constructed and analyzed to find the adiabatic invariants, from which the basic parameters of the focusing system can be calculated.     

基于通用运动控制器的磁场点测台控制系统

磁场点测台是加速器领域测量磁铁和波荡器等磁元件的主要设备之一, 其需要在快速精确的控制系统支持下工作。中国工程物理研究院应用电子学研究所近期搭建了一套磁场点测台, 并基于通用运动控制器(UMAC), 设计开发了该磁场点测台的控制系统。系统采用了上位机工控机和下位机UMAC两级计算机控制的层级结构, 可以充分发挥其各自优势: 下位机UMAC可以快速、精确地控制电机动作, 因此下位机程序负责控制六轴运动平台以go-stop模式运动; 上位机工控机数据处理和存储能力强, 因此上位机人机交互界面负责收集、记录和显示磁场数据, 并负责设定磁场测量参数和监控运行状态。两级计算机动作的同时性通过触发信号来保证。     

Two-dimensional exciton-phonon system in a magnetic field

The properties of an exciton at the surface of a polar crystal in a weak magnetic fieldB, which is perpendicular to the surface and is constant, are discussed by a perturbational method. Taking account of the effects from the surface modes of the lattice vibrations and on ground of a slow motion of the exciton, the self-energy of an exciton, the effective potential and renormalized masses are derived. The self-energy of the exciton becomes higher under the action of the magnetic field.Center of Theoretical Physics, CCAST (World Laboratory)