7,367 research outputs found
The Refractive Index of Curved Spacetime: the Fate of Causality in QED
It has been known for a long time that vacuum polarization in QED leads to a
superluminal low-frequency phase velocity for light propagating in curved
spacetime. Assuming the validity of the Kramers-Kronig dispersion relation,
this would imply a superluminal wavefront velocity and the violation of
causality. Here, we calculate for the first time the full frequency dependence
of the refractive index using world-line sigma model techniques together with
the Penrose plane wave limit of spacetime in the neighbourhood of a null
geodesic. We find that the high-frequency limit of the phase velocity (i.e. the
wavefront velocity) is always equal to c and causality is assured. However, the
Kramers-Kronig dispersion relation is violated due to a non-analyticity of the
refractive index in the upper-half complex plane, whose origin may be traced to
the generic focusing property of null geodesic congruences and the existence of
conjugate points. This puts into question the issue of micro-causality, i.e.
the vanishing of commutators of field operators at spacelike separated points,
in local quantum field theory in curved spacetime.Comment: 43 pages, 19 figures, JHEP3, conclusions respecting microcausality
modifie
`Superluminal' Photon Propagation in QED in Curved Spacetime is Dispersive and Causal
It is now well-known that vacuum polarisation in QED can lead to superluminal
low-frequency phase velocities for photons propagating in curved spacetimes. In
a series of papers, we have shown that this quantum phenomenon is dispersive
and have calculated the full frequency dependence of the refractive index,
explaining in detail how causality is preserved and various familiar results
from quantum field theory such as the Kramers-Kronig dispersion relation and
the optical theorem are realised in curved spacetime. These results have been
criticised in a recent paper by Akhoury and Dolgov arXiv:1003.6110 [hep-th],
who assert that photon propagation is neither dispersive nor necessarily
causal. In this note, we point out a series of errors in their work which have
led to this false conclusion.Comment: 11 page
Causality and Micro-Causality in Curved Spacetime
We consider how causality and micro-causality are realised in QED in curved
spacetime. The photon propagator is found to exhibit novel non-analytic
behaviour due to vacuum polarization, which invalidates the Kramers-Kronig
dispersion relation and calls into question the validity of micro-causality in
curved spacetime. This non-analyticity is ultimately related to the generic
focusing nature of congruences of geodesics in curved spacetime, as implied by
the null energy condition, and the existence of conjugate points. These results
arise from a calculation of the complete non-perturbative frequency dependence
of the vacuum polarization tensor in QED, using novel world-line path integral
methods together with the Penrose plane-wave limit of spacetime in the
neighbourhood of a null geodesic. The refractive index of curved spacetime is
shown to exhibit superluminal phase velocities, dispersion, absorption (due to
\gamma \to e^+e^-) and bi-refringence, but we demonstrate that the wavefront
velocity (the high-frequency limit of the phase velocity) is indeed c, thereby
guaranteeing that causality itself is respected.Comment: 16 pages, 11 figures, JHEP3, microcausality now shown to be respected
even when the Kramers-Kronig relation is violate
Graviton Propagation and Vacuum Polarization in Curved Space
The effects of vacuum polarization arising from loops of massive scalar
particles on graviton propagation in curved space are considered. Physically,
they are due to curvature induced tidal forces acting on the cloud of virtual
scalar particles surrounding the graviton. The effects are tractable in a WKB
and large mass limit and the results can be written as an effective refractive
index for the graviton modes with both a real and imaginary part. The imaginary
part of the refractive index is a curvature induced contribution to the
wavefunction renormalization of the graviton in real affine time and can have
the effect of dressing or un-dressing the graviton. The real part of the
refractive index increases logarithmically at high frequency as long as the
null energy condition is satisfied by the background.Comment: 21 pages, typos correcte
Generalized molecular chaos hypothesis and H-theorem: Problem of constraints and amendment of nonextensive statistical mechanics
Quite unexpectedly, kinetic theory is found to specify the correct definition
of average value to be employed in nonextensive statistical mechanics. It is
shown that the normal average is consistent with the generalized
Stosszahlansatz (i.e., molecular chaos hypothesis) and the associated
H-theorem, whereas the q-average widely used in the relevant literature is not.
In the course of the analysis, the distributions with finite cut-off factors
are rigorously treated. Accordingly, the formulation of nonextensive
statistical mechanics is amended based on the normal average. In addition, the
Shore-Johnson theorem, which supports the use of the q-average, is carefully
reexamined, and it is found that one of the axioms may not be appropriate for
systems to be treated within the framework of nonextensive statistical
mechanics.Comment: 22 pages, no figures. Accepted for publication in Phys. Rev.
A method to measure vacuum birefringence at FCC-ee
It is well-known that the Heisenberg-Euler-Schwinger effective Lagrangian
predicts that a vacuum with a strong static electromagnetic field turns
birefringent. We propose a scheme that can be implemented at the planned
FCC-ee, to measure the nonlinear effect of vacuum birefringence in
electrodynamics arising from QED corrections. Our scheme employs a pulsed laser
to create Compton backscattered photons off a high energy electron beam, with
the FCC-ee as a particularly interesting example. These photons will pass
through a strong static magnetic field, which changes the state of polarization
of the radiation - an effect proportional to the photon energy. This change
will be measured by the use of an aligned single-crystal, where a large
difference in the pair production cross-sections can be achieved. In the
proposed experimental setup the birefringence effect gives rise to a difference
in the number of pairs created in the analyzing crystal, stemming from the fact
that the initial laser light has a varying state of polarization, achieved with
a rotating quarter wave plate. Evidence for the vacuum birefringent effect will
be seen as a distinct peak in the Fourier transform spectrum of the
pair-production rate signal. This tell-tale signal can be significantly above
background with only few hours of measurement, in particular at high energies.Comment: Presented by UIU at the International Symposium on "New Horizons in
Fundamental Physics: From Neutrons Nuclei via Superheavy Elements and
Supercritical Fields to Neutron Stars and Cosmic Rays," held to honor Walter
Greiner on his 80th birthday at Makutsi Safari Farm, South Africa, November
23-29, 201
Non-universal coarsening and universal distributions in far-from equilibrium systems
Anomalous coarsening in far-from equilibrium one-dimensional systems is
investigated by simulation and analytic techniques. The minimal hard core
particle (exclusion) models contain mechanisms of aggregated particle
diffusion, with rates epsilon<<1, particle deposition into cluster gaps, but
suppressed for the smallest gaps, and breakup of clusters which are adjacent to
large gaps. Cluster breakup rates vary with the cluster length x as kx^alpha.
The domain growth law x ~ (epsilon t)^z, with z=1/(2+alpha) for alpha>0, is
explained by a scaling picture, as well as the scaling of the density of double
vacancies (at which deposition and cluster breakup are allowed) as 1/[t(epsilon
t)^z]. Numerical simulations for several values of alpha and epsilon confirm
these results. An approximate factorization of the cluster configuration
probability is performed within the master equation resulting from the mapping
to a column picture. The equation for a one-variable scaling function explains
the above results. The probability distributions of cluster lengths scale as
P(x)= 1/(epsilon t)^z g(y), with y=x/(epsilon t)^z. However, those
distributions show a universal tail with the form g(y) ~ exp(-y^{3/2}), which
disagrees with the prediction of the independent cluster approximation. This
result is explained by the connection of the vacancy dynamics with the problem
of particle trapping in an infinite sea of traps and is confirmed by
simulation.Comment: 30 pages (10 figures included), to appear in Phys. Rev.
Phase shifts in nonresonant coherent excitation
Far-off-resonant pulsed laser fields produce negligible excitation between
two atomic states but may induce considerable phase shifts. The acquired phases
are usually calculated by using the adiabatic-elimination approximation. We
analyze the accuracy of this approximation and derive the conditions for its
applicability to the calculation of the phases. We account for various sources
of imperfections, ranging from higher terms in the adiabatic-elimination
expansion and irreversible population loss to couplings to additional states.
We find that, as far as the phase shifts are concerned, the adiabatic
elimination is accurate only for a very large detuning. We show that the
adiabatic approximation is a far more accurate method for evaluating the phase
shifts, with a vast domain of validity; the accuracy is further enhanced by
superadiabatic corrections, which reduce the error well below .
Moreover, owing to the effect of adiabatic population return, the adiabatic and
superadiabatic approximations allow one to calculate the phase shifts even for
a moderately large detuning, and even when the peak Rabi frequency is larger
than the detuning; in these regimes the adiabatic elimination is completely
inapplicable. We also derive several exact expressions for the phases using
exactly soluble two-state and three-state analytical models.Comment: 10 pages, 7 figure
Stimulated Raman adiabatic passage analogs in classical physics
Stimulated Raman adiabatic passage (STIRAP) is a well established technique
for producing coherent population transfer in a three-state quantum system. We
here exploit the resemblance between the Schrodinger equation for such a
quantum system and the Newton equation of motion for a classical system
undergoing torque to discuss several classical analogs of STIRAP, notably the
motion of a moving charged particle subject to the Lorentz force of a
quasistatic magnetic field, the orientation of a magnetic moment in a slowly
varying magnetic field, the Coriolis effect and the inertial frame dragging
effect. Like STIRAP, those phenomena occur for counterintuitively ordered field
pulses and are robustly insensitive to small changes in the interaction
properties
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