580 research outputs found
Electron vortex beams in a magnetic field: A new twist on Landau levels and Aharonov-Bohm states
We examine the propagation of the recently-discovered electron vortex beams
in a longitudinal magnetic field. We consider both the Aharonov-Bohm
configuration with a single flux line and the Landau case of a uniform magnetic
field. While stationary Aharonov-Bohm modes represent Bessel beams with flux-
and vortex-dependent probability distributions, stationary Landau states
manifest themselves as non-diffracting Laguerre-Gaussian beams. Furthermore,
the Landau-state beams possess field- and vortex-dependent phases: (i) the
Zeeman phase from coupling the quantized angular momentum to the magnetic field
and (ii) the Gouy phase, known from optical Laguerre-Gaussian beams.
Remarkably, together these phases determine the structure of Landau energy
levels. This unified Zeeman-Landau-Gouy phase manifests itself in a nontrivial
evolution of images formed by various superpositions of modes. We demonstrate
that, depending on the chosen superposition, the image can rotate in a magnetic
field with either (i) Larmor, (ii) cyclotron (double-Larmor), or (iii) zero
frequency. At the same time, its centroid always follows the classical
cyclotron trajectory, in agreement with the Ehrenfest theorem. Remarkably, the
non-rotating superpositions reproduce stable multi-vortex configurations that
appear in rotating superfluids. Our results open up an avenue for the direct
electron-microscopy observation of fundamental properties of free quantum
electron states in magnetic fields.Comment: 21 pages, 10 figures, 1 table, to appear in Phys. Rev.
Deformation and Depinning of Superconducting Vortices from Artificial Defects: A Ginzburg-Landau Study
Using Ginzburg-Landau theory, we have performed detailed studies of vortices
in the presence of artificial defect arrays, for a thin film geometry. We show
that when a vortex approaches the vicinity of a defect, an abrupt transition
occurs in which the vortex core develops a ``string'' extending to the defect
boundary, while simultaneously the supercurrents and associated magnetic flux
spread out and engulf the defect. Current induced depinning of vortices is
shown to be dominated by the core string distortion in typical experimental
situations. Experimental consequences of this unusual depinning behavior are
discussed.Comment: 10 pages,9 figure
A hybrid learning algorithm for multilayer perceptrons to improve generalization under sparse training data conditions
The back-propagation algorithm is mainly used for multilayer perceptrons. This algorithm is, however, difficult to achieve high generalization when the number of training data is limited, that is sparse training data. In this paper, a new learning algorithm is proposed. It combines the BP algorithm and modifies hyperplanes taking internal information into account. In other words, the hyperplanes are controlled by the distance between the hyperplanes and the critical training data, which locate close to the boundary. This algorithm works well for the sparse training data to achieve high generalization. In order to evaluate generalization, it is supposed that all data are normally distributed around the training data. Several simulations of pattern classification demonstrate efficiency of the proposed
Phase Coherence in Quantum Brownian Motion
The quantum theory of Brownian motion is discussed in the Schwinger version
wherein the notion of a coordinate moving forward in time is replaced by
two coordinates, moving forward in time and moving backward
in time. The role of the doubling of the degrees of freedom is illustrated for
the case of electron beam two slit diffraction experiments. Interference is
computed with and without dissipation (described by a thermal bath). The notion
of a dissipative interference phase, closely analogous to the Aharonov-Bohm
magnetic field induced phase, is explored.Comment: 12 pages, LaTeX, 2 Figure
Darwin-Lagrangian Analysis for the Interaction of a Point Charge and a Magnet: Considerations Related to the Controversy Regarding the Aharonov-Bohm and Aharonov-Casher Phase Shifts
The classical electromagnetic interaction of a point charge and a magnet is
discussed by first calculating the interaction of point charge with a simple
model magnetic moment and then suggesting a multiparticle limit. The Darwin
Lagrangian is used to analyze the electromagnetic behavior of the model
magnetic moment (composed of two oppositely charged particles of different mass
in an initially circular orbit) interacting with a passing point charge. The
changing mangetic moment is found to put a force back on a passing charge; this
force is of order 1/c^2 and depends upon the magnitude of the magnetic moment.
It is suggested that in the limit of a multiparticle magnetic toroid, the
electric fields of the passing charge are screened out of the body of the
magnet while the magnetic fields penetrate into the magnet. This is consistent
with our understanding of the penetration of electromagnetic velocity fields
into ohmic conductors. Conservation laws are discussed. The work corresponds to
a classical electromagnetic analysis of the interaction which is basic to
understanding the controversy over the Aharonov-Bohm and Aharonov-Casher phase
shifts and represents a refutation of the suggestions of Aharonov, Pearle, and
Vaidman.Comment: 33 page
Aharonov-Bohm interference in the presence of metallic mesoscopic cylinders
This work studies the interference of electrons in the presence of a line of
magnetic flux surrounded by a normal-conducting mesoscopic cylinder at low
temperature. It is found that, while there is a supplementary phase
contribution from each electron of the mesoscopic cylinder, the sum of these
individual supplementary phases is equal to zero, so that the presence of a
normal-conducting mesoscopic ring at low temperature does not change the
Aharonov-Bohm interference pattern of the incident electron. It is shown that
it is not possible to ascertain by experimental observation that the shielding
electrons have responded to the field of an incident electron, and at the same
time to preserve the interference pattern of the incident electron. It is also
shown that the measuring of the transient magnetic field in the region between
the two paths of an electron interference experiment with an accuracy at least
equal to the magnetic field of the incident electron generates a phase
uncertainty which destroys the interference pattern.Comment: 15 pages, 5 Postscript figure
Recommended from our members
Electron Holography of Electromagnetic Fields - Recent Theoretical Advances.
It has been shown in this work that the Fourier space approach can be fruitfully applied to the calculation of the fields and the associated electron optical phase shift of several magnetic and electrostatic structures, like superconducting vortices in conventional and high-T{sub c} superconductors, reverse biased p-n junctions, magnetic domains and nanoparticles. In all these cases, this novel approach has led to unexpected but extremely interesting results, very often expressed in analytical form, which allow the quantitative and reliable interpretation of the experimental data collected by means of electron holography or of more conventional Lorentz microscopy techniques. Moreover, it is worth recalling that whenever long-range electromagnetic fields are involved, a physical model of the object under investigation is necessary in order to take into account correctly the perturbation of the reference wave induced by the tail of the field protruding into the vacuum. For these reasons, we believe that the Fourier space approach for phase computations we have introduced and discussed in this chapter will represent an invaluable tool for the investigation of electromagnetic fields at the meso- and nano-scale
Quantum Interference in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals
We investigate analytically and numerically the mean-field
superconducting-normal phase boundaries of two-dimensional superconducting wire
networks and Josephson junction arrays immersed in a transverse magnetic field.
The geometries we consider include square, honeycomb, triangular, and kagome'
lattices. Our approach is based on an analytical study of multiple-loop
Aharonov-Bohm effects: the quantum interference between different electron
closed paths where each one of them encloses a net magnetic flux. Specifically,
we compute exactly the sums of magnetic phase factors, i.e., the lattice path
integrals, on all closed lattice paths of different lengths. A very large
number, e.g., up to for the square lattice, exact lattice path
integrals are obtained. Analytic results of these lattice path integrals then
enable us to obtain the resistive transition temperature as a continuous
function of the field. In particular, we can analyze measurable effects on the
superconducting transition temperature, , as a function of the magnetic
filed , originating from electron trajectories over loops of various
lengths. In addition to systematically deriving previously observed features,
and understanding the physical origin of the dips in as a result of
multiple-loop quantum interference effects, we also find novel results. In
particular, we explicitly derive the self-similarity in the phase diagram of
square networks. Our approach allows us to analyze the complex structure
present in the phase boundaries from the viewpoint of quantum interference
effects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure
Nonlocal Phases of Local Quantum Mechanical Wavefunctions in Static and Time-Dependent Aharonov-Bohm Experiments
We show that the standard Dirac phase factor is not the only solution of the
gauge transformation equations. The full form of a general gauge function (that
connects systems that move in different sets of scalar and vector potentials),
apart from Dirac phases also contains terms of classical fields that act
nonlocally (in spacetime) on the local solutions of the time-dependent
Schr\"odinger equation: the phases of wavefunctions in the Schr\"odinger
picture are affected nonlocally by spatially and temporally remote magnetic and
electric fields, in ways that are fully explored. These contributions go beyond
the usual Aharonov-Bohm effects (magnetic or electric). (i) Application to
cases of particles passing through static magnetic or electric fields leads to
cancellations of Aharonov-Bohm phases at the observation point; these are
linked to behaviors at the semiclassical level (to the old Werner & Brill
experimental observations, or their "electric analogs" - or to recent reports
of Batelaan & Tonomura) but are shown to be far more general (true not only for
narrow wavepackets but also for completely delocalized quantum states). By
using these cancellations, certain previously unnoticed sign-errors in the
literature are corrected. (ii) Application to time-dependent situations
provides a remedy for erroneous results in the literature (on improper uses of
Dirac phase factors) and leads to phases that contain an Aharonov-Bohm part and
a field-nonlocal part: their competition is shown to recover Relativistic
Causality in earlier "paradoxes" (such as the van Kampen thought-experiment),
while a more general consideration indicates that the temporal nonlocalities
found here demonstrate in part a causal propagation of phases of quantum
mechanical wavefunctions in the Schr\"odinger picture. This may open a direct
way to address time-dependent double-slit experiments and the associated causal
issuesComment: 49 pages, 1 figure, presented in Conferences "50 years of the
Aharonov-Bohm effect and 25 years of the Berry's phase" (Tel Aviv and
Bristol), published in Journ. Phys. A. Compared to the published paper, this
version has 17 additional lines after eqn.(14) for maximum clarity, and the
Abstract has been slightly modified and reduced from the published 2035
characters to the required 1920 character
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