Connecting solutions of the Lorentz force equation do exist

Periodic solutions for the Lorentz force equation with singular potentials

We provide sufficient conditions for the existence of periodic solutions of the of the Lorentz force equation, which models the motion of a charged particle under the action of an electromagnetic fields. The basic assumptions cover relevant models with singularities like Coulomb-like electric potentials or the magnetic dipole.

Spinor extended Lorentz-force like equations as consequence of a spinorial structure of space-time

As previously shown, the special relativistic dynamical equation of the Lorentz force type can be regarded as a consequence of a succession of space-time dependent infinitesimal Lorentz boosts and rotations. This insight indicate that the Lorentz-Force-like equation has a fundamental meaning in physics. We show how this result may be spinorially obtained starting out out from the application of an infinitesimal element of SL(2,C) to the individual spinors, which are regarded here as being more fundamental objects than four-vectors. In this way we get a set of new dynamical spinor equations ind…

The ponderomotive Lorentz force

This paper describes a curious phenomenon: a particle in a rapidly varying potential is subject to an effective magnetic-like force. This force is in addition to the well-known ponderomotive force, but it has not been shown to exist before except for the linear case of a rapidly rotating quadratic saddle potential. We show that this is a universal phenomenon: the magnetic-like force arises generically in potential force fields with rapid periodic time dependence, including but not limited to rotational dependence.

The Lorentz Force Law and Spacetime Symmetries

Assume that arc length is measured with the flat spacetime metric. Then, for the most general Poincare group representation for translating 4-vectors, curves with parallel translated tangent vectors must have accelerations that are the scalar product of the tangent vector with an antisymmetric tensor. Such curves are the paths of charged particles in an electromagnetic field.

Fiber averaged dynamics associated with the Lorentz force equation

It is shown that the Lorentz force equation is equivalent to the auto-parallel condition $\,^L\nabla_{\dot{x}}\dot{x}=0$ of a linear connection $^L\nabla$ defined on a convenient pull-back vector bundle. By using a geometric averaging method, an associated {\it averaged Lorentz connection} $\langle\,^L\nabla\rangle$ and the corresponding auto-parallel equation are obtained. After this, it is shown that in the ultra-relativistic limit and for narrow one-particle probability distribution functions, the auto-parallel curves of $\langle\,^L\nabla\rangle$ remain {\it nearby} close to the auto-paral…

磁场中电子所受的约束哈密顿动力学及除洛伦兹力之外作用于电子的其他力

Constrained Hamiltonian dynamics for electrons in magnetic field and additional forces besides the Lorentz force acting on electrons

本文基于量子力学多体波函数和贝里联络，研究磁场中电子所受的约束动力学，揭示除洛伦兹力外还存在速度场动能梯度、化学势梯度及拓扑保护环电流相关的力，并阐明它们在超导、导线电流和电容器充电中的重要作用。

Effective dynamics for solitons in the nonlinear Klein Gordon Maxwell system and the Lorentz force law

We consider the nonlinear Klein Gordon Maxwell system on four dimensional Minkowski space-time. For appropriate nonlinearities the system admits soliton solutions which are gauge invariant generalizations of the non-topological solitons introduced and studied by T.D. Lee and collaborators for pure complex scalar fields. We develop a rigorous dynamical perturbation theory for these solitons in the small e limit, where e is the electromagnetic coupling constant. The main theorems assert the long time stability of the solitons with respect to perturbation by an external electromagnetic field prod…

具主导向量势的洛伦兹力方程的作用量极小化周期轨道

Action-minimizing periodic orbits of the Lorentz force equation with dominant vector potential

该研究通过极小化相对论拉格朗日量相关的作用量泛函，证明了具主导向量势的洛伦兹力方程存在非常数周期解，结果可推广至含可能奇异标势的情形，还利用向量势项的符号不定性证明了泛函负值的存在性。

The classical Maxwell-Lorentz electrodynamics aspects of the electron inertia problem within the Feynman proper time paradigm

The Maxwell electromagnetic and the Lorentz type force equations are derived in the framework of the R. Feynman proper time paradigm and the related vacuum field theory approach. The electron inertia problem is analyzed within the Lagrangian and Hamiltonian formalisms and the related pressure-energy compensation principle. The modified Abraham- Lorentz damping radiation force is derived, the electromagnetic electron mass origin is argued.

Fluctuation of the entropy production for the Lorentz gas under small external forces

In this paper we study the physical and statistical properties of the periodic Lorentz gas with finite horizon driven to a non-equilibrium steady state by the combination of non-conservative external forces and deterministic thermostats. A version of this model was introduced by Chernov, Eyink, Lebowitz, and Sinai and subsequently generalized by Chernov and the third author. Non-equilibrium steady states for these models are SRB measures and they are characterized by the positivity of the steady state entropy production rate. Our main result is to establish that the entropy production, in this…

Electromagnetic Force as consequence of the Geometry of Minkowskian Spacetime

By describing the dynamical evolution of a test charged particle in the presence of an electromagnetic field as a succession of infinitesimal Lorentz boosts and rotations it is possible to obtain the Lorentz Force of Electrodynamics. A consequence of this derivation at the classical level is that, given the existence of electric and magnetic fields, the form of the electromagnetic force acting on the particle can be regarded as arising from the geometry of Minkowskian spacetime.