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.     

Interaction of radiation and a relativistic electron in motion in a constant magnetic field

This paper examines the effect of multiple photon emission on the quantum mechanical state of an electron emitting synchrotron radiation and on the intensity of that radiation. Calculations are done with a variant of perturbation theory based on the use of extended coherent states. A general formula is derived for the number of emitted photons, which allows taking into account their mutual interaction. A model problem is used to demonstrate the absence of the infrared catastrophe in the modified perturbation theory. Finally, the electron density matrix is calculated, and the analysis of this matrix makes it possible to conclude that the degree of the electron’s spatial localization increases with the passage of time if the electron is being accelerated. Zh. éksp. Teor. Fiz. 113, 841–864 (March 1998)     

Limits on stability of positive molecular ions in a homogeneous magnetic field

The problem of stability of positive diatomic molecular ions with the nuclear chargesZ ₁ andZ ₂ andN electrons in a homogeneous magnetic fieldB is studied forZ ₁,Z ₂,N,B. The conditions of instability are obtained for different relations amongZ ₁,Z ₂,N andB. A new version of the HVZ theorem for systems in a homogeneous magnetic field is proved.Supported by the International Erwin Schrödinger Institute, Austria, International Science Foundation Grant N R 94000 and Grant of Russian Fond Fudament. Issled. 94-01-01376.     

Interpretation of quantum numbers in the problem of charge motion in a constant uniform magnetic field

A physical interpretation of quantum numbers in the problem of charge motion in a constant uniform magnetic field is made. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 12–18, August, 2008.     

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.     

An approximate calculation of the non-adiabatic motion of a charged particle in an inhomogeneous rotationally symmetric magnetic field

A study is made of the motion of a particle injected longitudinally into a rotationally symmetric magnetic field increasing linearly in an arbitrarily sharp way on the axis of symmetry. By expanding the magnetic potential in a series in the vicinity of the line of force from which the particle starts, and by restricting our considerations to linear terms, we arrive at a single linearized equation of motion for the radial motion, as we assume the longitudinal motion to be uniform. The linearized equation can be solved exactly. Numerical evaluation is carried out (with the linearized line of force) for several different slopes of the field, and compared for similar cases with a numerical evaluation of an exact nonlinear problem. The method described in the paper can also be applied to cases with more general initial conditions, when the particle also moves with an azimuthal velocity.The author extends his thanks for valuable advice, discussions and encouragement to Dr. M. Seidl, on whose incentive the work was undertaken and who is the author of equation (13).     

Two-dimensional spherical oscillator in a constant magnetic field

We study the equations of motion of a spherical oscillator model suggested by Bellucci and Nersessian, in the presence of a constant magnetic field. This model is shown to be exactly solvable classically in contrast to the Higgs oscillator which is not exactly solvable in magnetic fields.     

Light-induced drift of ions in a magnetic field

The effect of a magnetic field on the ion drift in a weakly ionized gas under the combined action of the light-induced drift and light pressure is studied theoretically. It is shown that, under the action of light, a component of ion drift velocity transverse to the direction of propagation of radiation may appear in a weakly ionized gas upon the application of an external magnetic field. It is shown that the Lorentz force acting on ions in the magnetic field radically changes the dependence of the ion drift velocity on the radiation frequency detuning. It is predicted that the ion drift velocity component along the direction of radiation must reverse its sign upon an increase in the magnetic field and an anomalous light-induced drift may be observed.     

Deformation of solid polymers in a constant magnetic field

The effect of a constant magnetic field on the creep rate is investigated for poly(vinyl butyral), styrene-methacrylic acid copolymer [poly(styrene) + 16 wt % methacrylic acid], poly(methylene oxide), and other polymers. It is demonstrated that the constant magnetic field can variously affect different polymers and that the effect of the magnetic field is enhanced in a particular range of strain rates.     

Bohlin transformation for a two-dimensional singular oscillator in a constant magnetic field

Bohlin transformation for a circular singular oscillator in a constant magnetic field is considered. It is shown that this transformation leads to a two-dimensional Kepler problem with an additional centrifugal potential from the constant magnetic field whose strength decreases inversely proportional to the distance from the center of attraction of the system. The energy spectrum of the considered system is obtained.     

Rotamak中离子运动对旋转磁场电流驱动的影响

研究了旋转磁场电流驱动理论模型中离子运动的影响。考虑无限长的等离子体柱,在二维(r, θ)磁流体理论模型的基础上,采用电子运动方程和离子运动方程,并考虑离子的径向运动速度,建立了新的二维磁流体理论模型。然后把得出的结果与离子静止模型下的结果进行比较,并讨论了相应的物理过程。这个模型同样适用于平行于磁场线(Z方向)的流动效应和场旋转位形的压力平衡的理论计算。     

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.     

CN-Smorodinsky–Winternitz system in a constant magnetic field

We propose the superintegrable generalization of Smorodinsky–Winternitz system on the N-dimensional complex Euclidian space which is specified by the presence of constant magnetic field. We find out that in addition to 2N Liouville integrals the system has additional functionally independent constants of motion, and compute their symmetry algebra. We perform the Kustaanheimo–Stiefel transformation of ${\mathbb{C}}^2$-Smorodinsky–Winternitz system to the (three-dimensional) generalized MICZ-Kepler problem and find the symmetry algebra of the latter one. We observe that constant magnetic field appearing in the initial system has no qualitative impact on the resulting system.     

Resonance acceleration of ions in a variable magnetic field

The motion of a particle is considered in a variable magnetic field — the superposition of a driving field H(t) and a weak field oscillating at the frequency =eH(t)/mc. The law of motion is found by the averaging method, and it is shown that the particle energy increases exponentially.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 75–78, October, 1978.In conclusion, thanks are due to the participants in Prof. Sokolov's seminar for discussion of the work.     

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     

Decay of a negative molecular ion in a constant electric field

The problem of the shift and broadening of the electron energy levels in the field of two 3D short-range potentials (e.g., the model of a negative molecular ion) by a constant electric field F is considered. The interaction of an electron with attraction centers is taken into account in the effective range approximation. We analyze the cases when both centers maintain weakly bound s states and when the electron state in the field of one of the centers is a p state. Exact numerical results for the shift and the width of the energy levels of a quasi-molecule as functions of field F, distance R between atomic centers, and the orientation of the quasi-molecule axis relative to vector F are presented, as well as the results of analytic treatment for a number of limiting cases. The exact values of complex energies of the quasi-molecule are compared with analytic results for a weak field in the case of identical s centers [26], as well as nonequivalent s centers and s-p centers; the applicability boundaries of the weak field approximation are established. It is shown that for large values of R, the position and width of the levels in a strong field are correctly described in perturbation theory in the exchange interaction. We analyze the field-induced quasi-intersection of molecular energy levels of the system with nonequivalent atomic centers and peculiarities in the energy level widths associated with this intersection. The results make it possible to qualitatively interpret the results of numerical calculations of the probability of homo- and heteronuclear molecules being ionized by a low-frequency laser field.     

Discrete accidental symmetry for a particle in a constant magnetic field on a torus

A classical particle in a constant magnetic field undergoes cyclotron motion on a circular orbit. At the quantum level, the fact that all classical orbits are closed gives rise to degeneracies in the spectrum. It is well-known that the spectrum of a charged particle in a constant magnetic field consists of infinitely degenerate Landau levels. Just as for the 1/r and r² potentials, one thus expects some hidden accidental symmetry, in this case with infinite-dimensional representations. Indeed, the position of the center of the cyclotron circle plays the role of a Runge-Lenz vector. After identifying the corresponding accidental symmetry algebra, we re-analyze the system in a finite periodic volume. Interestingly, similar to the quantum mechanical breaking of CP invariance due to the θ-vacuum angle in non-Abelian gauge theories, quantum effects due to two self-adjoint extension parameters θ_x and θ_y explicitly break the continuous translation invariance of the classical theory. This reduces the symmetry to a discrete magnetic translation group and leads to finite degeneracy. Similar to a particle moving on a cone, a particle in a constant magnetic field shows a very peculiar realization of accidental symmetry in quantum mechanics.