97 research outputs found
Design of a test for the electromagnetic coupling of non-local wavefunctions
It has recently been proven that certain effective wavefunctions in
fractional quantum mechanics and condensed matter do not have a locally
conserved current; as a consequence, their coupling to the electromagnetic
field leads to extended Maxwell equations, featuring non-local, formally simple
additional source terms. Solving these equations in general form or finding
analytical approximations is a formidable task, but numerical solutions can be
obtained by performing some bulky double-retarded integrals. We focus on
concrete experimental situations which may allow to detect an anomalous
quasi-static magnetic field generated by these (collective) wavefunctions in
cuprate superconductors. We compute the spatial dependence of the field and its
amplitude as a function of microscopic parameters including the fraction
of supercurrent that is not locally conserved in Josephson junctions between
grains, the thickness of the junctions and the size of their
current sinks and sources. The results show that the anomalous field is
actually detectable at the macroscopic level with sensitive experiments, and
can be important at the microscopic level because of virtual charge effects
typical of the extended Maxwell equations.Comment: 17 pages, 5 figures - Final journal versio
Oscillating dipole with fractional quantum source in Aharonov-Bohm electrodynamics
We show, in the case of a special dipolar source, that electromagnetic fields
in fractional quantum mechanics have an unexpected space dependence:
propagating fields may have non-transverse components, and the distinction
between near-field zone and wave zone is blurred. We employ an extension of
Maxwell theory, Aharonov-Bohm electrodynamics, which is compatible with
currents conserved globally but not locally, we have derived in another
work the field equation , where
is a non-local function of , called "secondary current". Y.\ Wei has
recently proved that the probability current in fractional quantum mechanics is
in general not locally conserved. We compute this current for a Gaussian wave
packet with fractional parameter and find that in a suitable limit it
can be approximated by our simplified dipolar source. Currents which are not
locally conserved may be present also in other quantum systems whose wave
functions satisfy non-local equations. The combined electromagnetic effects of
such sources and their secondary currents are very interesting both
theoretically and for potential applications.Comment: 2 pages, 2 figure
Tunneling of a Massless Field through a 3D Gaussian Barrier
We propose a method for the approximate computation of the Green function of
a scalar massless field Phi subjected to potential barriers of given size and
shape in spacetime. This technique is applied to the case of a 3D gaussian
ellipsoid-like barrier, placed on the axis between two pointlike sources of the
field. Instead of the Green function we compute its temporal integral, that
gives the static potential energy of the interaction of the two sources. Such
interaction takes place in part by tunneling of the quanta of Phi across the
barrier. We evaluate numerically the correction to the potential in dependence
on the size of the barrier and on the barrier-sources distance.Comment: 16 pages, LaTeX, 3 PostScript figures; improved presentation, to
appear in J. Math. Phy
High-frequency electromagnetic emission from non-local wavefunctions
In systems with non-local potentials or other kinds of non-locality, the
Landauer-B\"uttiker formula of quantum transport leads to replace the usual
gauge-invariant current density with a current
which has a non-local part and coincides with the current of the extended
Aharonov-Bohm electrodynamics. It follows that the electromagnetic field
generated by this current can have some peculiar properties, and in particular
the electric field of an oscillating dipole can have a long-range longitudinal
component. The calculation is complex because it requires the evaluation of
double-retarded integrals. We report the outcome of some numerical integrations
with specific parameters for the source: dipole length cm,
frequency 10 GHz. The resulting longitudinal field turns out to be of the
order of to times larger than the transverse component (only for
the non-local part of the current). Possible applications concern the radiation
field generated by Josephson tunnelling in thick SNS junctions in YBCO and by
current flow in molecular nano-devices.Comment: 19 pages, 1 figur
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