511 research outputs found
Motion of vortex lines in nonlinear wave mechanics
We extend our previous analysis of the motion of vortex lines [I.
Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa, Phys. Rev. A 61, 032110
(2000)] from linear to a nonlinear Schroedinger equation with harmonic forces.
We also argue that under certain conditions the influence of the contact
nonlinearity on the motion of vortex lines is negligible. The present analysis
adds new weight to our previous conjecture that the topological features of
vortex dynamics are to a large extent universal.Comment: To appear in Phys. Rev. A, 4 page
Electromagnetic vortex lines riding atop null solutions of the Maxwell equations
New method of introducing vortex lines of the electromagnetic field is
outlined. The vortex lines arise when a complex Riemann-Silberstein vector
is multiplied by a complex scalar function
. Such a multiplication may lead to new solutions of the Maxwell
equations only when the electromagnetic field is null, i.e. when both
relativistic invariants vanish. In general, zeroes of the function give
rise to electromagnetic vortices. The description of these vortices benefits
from the ideas of Penrose, Robinson and Trautman developed in general
relativity.Comment: NATO Workshop on Singular Optics 2003 To appear in Journal of Optics
Heisenberg uncertainty relation for photons
The idea to base the uncertainty relation for photons on the electromagnetic
energy distribution in space enabled us to derive a sharp inequality that
expresses the uncertainty relation [Phys. Rev. Lett. {\bf 108}, 140401 (2012)].
An alternative version of the uncertainty relation derived in this paper is
closer in spirit to the original Heisenberg relation because it employs the
analog of the position operator for the photon---the center of energy operator.
The noncommutativity of the components of the center of energy operator results
in the increase of the bound in the standard Heisenberg
uncertainty relation in three dimensions. This difference diminishes with the
increase of the photon energy. In the limiting case of infinite momentum frame,
the lower bound in the Heisenberg uncertainty relations for photons is the same
as in nonrelativistic quantum mechanics.Comment: Sequel to PRL, 108, 140401 (2012); Submitted to PR
Squeezing of electromagnetic field in a cavity by electrons in Trojan states
The notion of the Trojan state of a Rydberg electron, introduced by
I.Bialynicki-Birula, M.Kali\'nski, and J.H.Eberly (Phys. Rev. Lett. 73, 1777
(1994)) is extended to the case of the electromagnetic field quantized in
acavity. The shape of the electronic wave packet describing the Trojan state is
practically the same as in the previously studied externally driven system. The
fluctuations of the quantized electromagnetic field around its classical value
exhibit strong squeezing. The emergence of Trojan states in the cylindrically
symmetrical system is attributed to spontaneous symmetry braking.Comment: 9 pages, 8 figure
Exponential beams of electromagnetic radiation
We show that in addition to well known Bessel, Hermite-Gauss, and
Laguerre-Gauss beams of electromagnetic radiation, one may also construct
exponential beams. These beams are characterized by a fall-off in the
transverse direction described by an exponential function of rho. Exponential
beams, like Bessel beams, carry definite angular momentum and are periodic
along the direction of propagation, but unlike Bessel beams they have a finite
energy per unit beam length. The analysis of these beams is greatly simplified
by an extensive use of the Riemann-Silberstein vector and the Whittaker
representation of the solutions of the Maxwell equations in terms of just one
complex function. The connection between the Bessel beams and the exponential
beams is made explicit by constructing the exponential beams as wave packets of
Bessel beams.Comment: Dedicated to the memory of Edwin Powe
Vortex lines of the electromagnetic field
Relativistic definition of the phase of the electromagnetic field, involving
two Lorentz invariants, based on the Riemann-Silberstein vector is adopted to
extend our previous study [I. Bialynicki-Birula, Z. Bialynicka-Birula and C.
Sliwa, Phys. Rev. A 61, 032110 (2000)] of the motion of vortex lines embedded
in the solutions of wave equations from Schroedinger wave mechanics to Maxwell
theory. It is shown that time evolution of vortex lines has universal features;
in Maxwell theory it is very similar to that in Schroedinger wave mechanics.
Connection with some early work on geometrodynamics is established. Simple
examples of solutions of Maxwell equations with embedded vortex lines are
given. Vortex lines in Laguerre-Gaussian beams are treated in some detail.Comment: 11 pages, 6 figures, to be published in Phys. Rev.
Dynamical Casimir effect in oscillating media
We show that oscillations of a homogeneous medium with constant material
coefficients produce pairs of photons. Classical analysis of an oscillating
medium reveals regions of parametric resonance where the electromagnetic waves
are exponentially amplified. The quantum counterpart of parametric resonance is
an exponentially growing number of photons in the same parameter regions. This
process may be viewed as another manifestation of the dynamical Casimir effect.
However, in contrast to the standard dynamical Casimir effect, photon
production here takes place in the entire volume and is not due to time
dependence of the boundary conditions or material constants
Pinning and transport of cyclotron/Landau orbits by electromagnetic vortices
Electromagnetic waves with phase defects in the form of vortex lines combined
with a constant magnetic field are shown to pin down cyclotron orbits (Landau
orbits in the quantum mechanical setting) of charged particles at the location
of the vortex. This effect manifests itself in classical theory as a trapping
of trajectories and in quantum theory as a Gaussian shape of the localized wave
functions. Analytic solutions of the Lorentz equation in the classical case and
of the Schr\"odinger or Dirac equations in the quantum case are exhibited that
give precise criteria for the localization of the orbits. There is a range of
parameters where the localization is destroyed by the parametric resonance.
Pinning of orbits allows for their controlled positioning -- they can be
transported by the motion of the vortex lines.Comment: This version differs from the printed paper in having the full titles
of all referenced pape
Electromagnetic radiation by gravitating bodies
Gravitating bodies in motion, regardless of their constitution, always
produce electromagnetic radiation in the form of photon pairs. This phenomenon
is an analog of the radiation caused by the motion of dielectric (or magnetic)
bodies. It is a member of a wide class of phenomena named dynamical Casimir
effects, and it may be viewed as the squeezing of the electromagnetic vacuum.
Production of photon pairs is a purely quantum-mechanical effect.
Unfortunately, as we show, the emitted radiation is extremely weak as compared
to radiation produced by other mechanisms.Comment: 6 page
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