14 research outputs found
The Effect of a Magnetic Flux Line in Quantum Theory
The nonloclal exchange of the conserved, gauge invariant quantity
between the charged particle and the magnetic flux line (in the
direction), is responsible for the Aharonov-Bohm effect. This exchange occurs
at a definite time, before the wavepackets are brought together to interfere,
and can be verified experimentally.Comment: LaTeX, 13 pages with 3 figure
A Novel Phase Shift Acquired due to Virtual Forces
This paper has been withdrawn by the author.Comment: This paper has been withdrawn by the author. 11 pages, 4 figure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
Quantum Measurement Back-Reaction and Induced Topological Phases
It is shown that a topological vector-potential (Berry phase) is induced by the act of measuring angular momentum in a direction defined by a reference particle. This vector potential appears as a consequence of the back-reaction due to the quantum measurement