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We consider an electron moving in a periodic potential and subject to an additional slowly varying external electrostatic potential, $\phi(\epsi x)$, and vector potential $A(\epsi x)$, with $x \in \R^d$ and $\epsi \ll 1$. We prove that…
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…
Investigating properties of two-dimensional Dirac operators coupled to an electric and a magnetic field (perpendicular to the plane) requires in general unbounded (vector-) potentials. If the system has a certain symmetry, the fields can be…
Dynamics of solitons of the Ablowitz-Ladik model in the presence of a random potential is studied. In absence of the random potential it is an integrable model and the solitons are stable. As a result of the random potential this stability…
We discuss the motion of electrically and magnetically charged particles in the electromagnetic swirling universe. We show that the equations of motion can be decoupled in the Hamilton-Jacobi formalism, revealing the existence of a fourth…
We revisit in the framework of the classical theory the problem of the accelerated motion of an electron, taking into account the effect of the radiation emission. We present results for the momentum and energy of the electromagnetic field…
We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors…
We find that a 2D periodic potential with different modulation amplitudes in x- and y-direction and a perpendicular magnetic field may lead to a transition to electron transport along the direction of stronger modulation and to localization…
Invariance under time translation (or stationarity) is probably one of the most important assumptions made when investigating electromagnetic phenomena. Breaking this assumption is expected to open up novel possibilities and result in…
We study the effects of the electromagnetic vacuum on the motion of a nonrelativistic electron. First, we derive the equation of motion for the expectation value of the electron's position operator. We show how this equation has the same…
The cyclic motion of particles in a periodic potential under the influence of a constant external force is analyzed in an atom optical approach based on Landau-Zener transitions between two resonant states. The resulting complex picture of…
In the present work, we study the classical behavior of an electric dipole in presence of an external uniform magnetic field. We derive equations and constants of motion from the Lagrangian formulation. We obtain an infinitely periodic…
We consider a quantum many-body model describing a system of electrons interacting with themselves and hopping from one ion to another of a one dimensional lattice. We show that the ground state energy of such system, as a functional of the…
The behaviour of an electron in a potential that resembles that of a bidimensional solid with a perpendicular magnetic field applied is studied from a classical point of view. This problem presents the standard features of chaos and some…
When particles move through a crystal or optical lattice, their motion can sometimes become frozen by strong external forces -- yet collective motion may still emerge through subtle many-body effects. In this work, we explore such…
We have identified ultra-cold atoms in magneto-optical double-well potentials as a very clean setting in which to study the quantum and classical dynamics of a nonlinear system with multiple degrees of freedom. In this system, entanglement…
On this article there are presented the main results of the theory of electron phenomena in an unordered condensed matter that can be described as an inhomogeneously deformed crystalline lattice with dislocations. The one-electron effective…
In this paper we consider the classical relativistic motion of charged particles in a knotted electromagnetic field. After reviewing how to construct electromagnetic knots from maps between the three-sphere and the two-sphere, we introduce…
In this paper we calculate and visualize the dynamics of an ensemble of electrons trapping in an electrostatic wave of slowly increasing amplitude, illustrating that, despite disordering of particles in angle during the trapping transition…
In this paper, we show how the motion of physical fields, in particular the electromagnetic potential, is connected with the choice of a space and time decomposition of the background spacetime manifold. The relation of the field dynamics…