Geometric Constructions Underlying Relativistic Description of Spin on the Base of Non-Grassmann Vector-Like Variable

Basic notions of Dirac theory of constrained systems have their analogs in differential geometry. Combination of the two approaches gives more clear understanding of both classical and quantum mechanics, when we deal with a model with complicated structure of constraints. In this work we describe and discuss the spin fiber bundle which appeared in various mechanical models where spin is described by vector-like variable

Frenkel electron on an arbitrary electromagnetic background and magnetic Zitterbewegung

We present Lagrangian which implies both necessary constraints and dynamical equations for position and spin of relativistic spin one-half particle. The model is consistent for any value of magnetic moment $\mu$ and for arbitrary electromagnetic background. Our equations coincide with those of Frenkel in the approximation in which the latter have been obtained by Frenkel. Transition from approximate to exact equations yields two structural modifications of the theory. First, Frenkel condition on spin-tensor turns into the Pirani condition. Second, canonical momentum is no more proportional to velocity. Due to this, even when $\mu=1$ (Frenkel case), the complete and approximate equations predict different behavior of particle. The difference between momentum and velocity means extra contribution into spin-orbit interaction. To estimate the contribution, we found exact solution to complete equations for the case of uniform magnetic field. While Frenkel electron moves around the circle, our particle experiences magnetic {\it Zitterbewegung}, that is oscillates in the direction of magnetic field with amplitude of order of Compton wavelength for the fast particle. Besides, the particle has dipole electric moment.Comment: 20 pages, 1 figure, close to published versio

Field-Dependent Critical Current in Type-II Superconducting Strips: Combined Effect of Bulk Pinning and Geometrical Edge Barrier

Recent theoretical and experimental research on low-bulk-pinning superconducting strips has revealed striking dome-like magnetic-field distributions due to geometrical edge barriers. The observed magnetic-flux profiles differ strongly from those in strips in which bulk pinning is dominant. In this paper we theoretically describe the current and field distributions of a superconducting strip under the combined influence of both a geometrical edge barrier and bulk pinning at the strip's critical current Ic, where a longitudinal voltage first appears. We calculate Ic and find its dependence upon a perpendicular applied magnetic field Ha. The behavior is governed by a parameter p, defined as the ratio of the bulk-pinning critical current Ip to the geometrical-barrier critical current Is0. We find that when p > 2/pi and Ip is field-independent, Ic vs Ha exhibits a plateau for small Ha, followed by the dependence Ic-Ip ~ 1/Ha in higher magnetic fields.Comment: 4 pages, 2 figures, Fig. 1 revised, submitted to Phys. Rev.

Non-linear quantum effects in electromagnetic radiation of a vortex electron

There is a controversy of how to interpret interactions of electrons with a large spatial coherence with light and matter. When such an electron emits a photon, it can do so either as if its charge were confined to a point within a coherence length, the region where a square modulus of a wave function $|\psi|^2$ is localized, or as a continuous cloud of space charge spread over it. This problem was addressed in a recent study R.~Remez, et al., Phys. Rev. Lett. {\bf 123}, 060401 (2019) where a conclusion was drawn in favor of the first (point) interpretation. Here we argue that there is an alternative explanation for the measurements reported in that paper, which relies on purely classical arguments and does not allow one to refute the second interpretation. We propose an experiment of Smith-Purcell radiation from a non-relativistic vortex electron carrying orbital angular momentum, which can unambiguously lead to the opposite conclusion. Beyond the paraxial approximation, the vortex packet has a non-point electric quadrupole moment, which grows as the packet spreads and results in a non-linear $L^3$-growth of the radiation intensity with the length $L$ of the grating when $L$ is much larger than the packet's Rayleigh length. Such a non-linear effect has never been observed for single electrons and, if detected, it would be a hallmark of the non-point nature of charge in a wave packet. Thus, two views on $|\psi|^2$ are complementary to each other and an electron radiates either as a point charge or as a continuous charge flow depending on the experimental conditions and on its quantum state. Our conclusions hold for a large class of non-Gaussian packets and emission processes for which the radiation formation length can exceed the Rayleigh length, such as Cherenkov radiation, transition radiation, diffraction radiation, and so forth.Comment: 25 pages; 4 figure

Manifestation of superfluidity in an evolving Bose-condensed gas

We study the generation of excitations due to an ''impurity''(static perturbation) placed into an oscillating Bose-condensed gas in the time-dependent trapping field. It is shown that there are two regions for the position of the local perturbation. In the first region the condensate flows around the ''impurity'' without generation of excitations demonstrating superfluid properties. In the second region the creation of excitations occurs, at least within a limited time interval, revealing destruction of superfluidity. The phenomenon can be studied by measuring the damping of condensate oscillations at different positions of the ''impurity''