arXiv subjects
Publications and source records attributed to J. Asch.
We study the dynamics of classical and quantum particles moving in a punctured plane under the influence of a homogeneous magnetic field and driven by a time-dependent singular flux tube through the hole.
We study the dynamics of a classical particle moving in a punctured plane under the influence of a strong homogeneous magnetic field, an electrical background, and driven by a time-dependent singular flux tube through the hole. We exhibit a striking classical (de)localization effect: in the far past the trajectories are spirals around a bound center; the particle moves inward towards the flux tube loosing kinetic energy. After hitting the puncture it becomes ``conducting'': the motion is a cycloid around a center whose drift is outgoing, orthogonal to the electric field, diffusive, and without energy loss.
We study the dynamics of a quantum particle moving in a plane under the influence of a constant magnetic field and driven by a slowly time-dependent singular flux tube through a puncture. The known adiabatic results do not cover these models as the Hamiltonian has time dependent domain. We give a meaning to the propagator and prove an adiabatic theorem. To this end we introduce and develop the new notion of a propagator weakly associated to a time-dependent Hamiltonian.
We derive the form of the asymptotic series, as $t\to +\infty$, for a general solution $h(t)$ of the non-linear differential equation $h(t)^{3}(h''(t)+h'(t))=1$.
We study the quantum dynamics generated by $H^{SW}=-{d^2\over dx^2}+V-x$ with $V$ a real periodic function of weak regularity. We prove that the continuous spectrum of $H^{SW}$ is never empty, and furthermore that for $V$ small enough there are no bound states.
We consider motion in a periodic potential in a classical, quantum, and semiclassical context. Various results on the distribution of asymptotic velocities are proven.