Antiparallele Weißsche Bereiche als Biprisma für Elektroneninterferenzen. II

On geometric interpretation of the Aharonov–Bohm effect

“…Contrary to this opinion, Aharonov and Bohm have demonstrated that the integral of a gauge field along a closed loop can produce the observable effects. The effect produced by the magnetic potential was soon confirmed experimentally [2,3,4].…”

“…Aharonov-Bohm phase difference (11) is uniquely defined by the contour γ (the same as for the electric potential) and values of the connection form A µ on it. Writing the contour integral in the form of surface integral (12), we assume that the connection is defined on the whole space-time R 4 . This means that we consider solenoid of finite radius to avoid singularities.…”

“…The metric η µν is defined only on spacelike sections t = const, because it enters the Schrödinger equation. The wave function ψ(t, x) is the section of the fiber bundle E R 4 , π E , C, U(1), P with the typical fiber being the complex plane C, which is associated with a certain principal fiber bundle P R 4 , π, U(1) . This principal fiber bundle is always trivial P ≈ R 4 × U(1), because its base is the four-dimensional Euclidean space.…”

Development of TEM Holder Generating In-Plane Magnetic Field Used for <i>In-Situ</i> TEM Observation

“…47) However, the patterns in this work is large, and the DW was expected to be thick (e.g., more than 100 nm) as has been reported for continuous Py films. 48,49) The MR effect due to the DW is quite small in such cases, 50) and thus the reduction in resistance is not caused by the DW itself. The local magnetization about a DW tends to be parallel (or antiparallel) to it as indicated by arrows in Figs.…”

Electron avalanche model of dielectric-vacuum surface breakdown

“…≤ A successful model should predict these characteristics Model Equations for Anode Tree Breakdown Fig 3 depicts a secondary electron orbit with initial momentum perpendicular to the surface and with En pushing the electron toward the dielectric. Boersch, Hamisch and Erlich analysed this motion in 1963 assuming the field components to be constant over the small dimensions of the orbit (2). Their equations are:…”