42 research outputs found
Light polarization oscillations induced by photon-photon scattering
We consider the Heisenberg-Euler action for an electromagnetic field in
vacuum, which includes quantum corrections to the Maxwell equations induced by
photon-photon scattering. We show that, in some configurations, the plane
monochromatic waves become unstable, due to the appearance of secularities in
the dynamical equations. These secularities can be treated using a multiscale
approach, introducing a slow time variable. The amplitudes of the plane
electromagnetic waves satisfy a system of ordinary differential nonlinear
equations in the slow time. The analysis of this system shows that, due to the
effect of photon-photon scattering, in the unstable configurations the
electromagnetic waves oscillate periodically between left-hand-sided and
right-hand-sided polarizations. Finally, we discuss the physical implications
of this finding, and the possibility of disclosing traces of this effect in
optical experiments.Comment: Version published in PRA, some typos correcte
Collective behavior of light in vacuum
Under the action of light-by-light scattering, light beams show collective
behaviors in vacuum. For instance, in the case of two counterpropagating laser
beams with specific initial helicity, the polarization of each beam oscillates
periodically between the left and right helicity. Furthermore, the amplitudes
and the corresponding intensities of each polarization propagate like waves.
Such polarization waves might be observationally accessible in future laser
experiments, in a physical regime complementary to those explored by particle
accelerators.Comment: Version published in Phys. Rev. A. arXiv admin note: text overlap
with arXiv:1710.0333
Interaction effects on atomic laboratory trapped Bose-Einstein condensates
We discuss the effect of inter-atoms interactions on the condensation
temperature of an atomic laboratory trapped Bose-Einstein condensate. We
show that, in the mean-field Hartree-Fock and semiclassical approximations,
interactions produce a shift with
the s-wave scattering length, the thermal wavelength and
a non-analytic function such that and . Therefore, with no more assumptions
than Hartree-Fock and semiclassical approximations, interaction effecs are
perturbative to second order in and the expected
non-perturbativity of physical quantities at critical temperature appears only
to third order. We compare this finding with different results by other
authors, which are based on more than the Hartree-Fock and semiclassical
approximations. Moreover, we obtain an analytical estimation for which improves a previous numerical result. We also discuss how the
discrepancy between and the empirical value of may be
explained with no need to resort to beyond-mean field effects.Comment: 6 pages, to appear in Eur. Phys. J. B (2013
Isochronous solutions of Einstein's equations and their Newtonian limit
It has been recently demonstrated that it is possible to construct
isochronous cosmologies, extending to general relativity a result valid for
non-relativistic Hamiltonian systems. In this paper we review these findings
and we discuss the Newtonian limit of these isochronous spacetimes, showing
that it reproduces the analogous findings in the context of non-relativistic
dynamics.Comment: arXiv admin note: text overlap with arXiv:1406.715
Isochronous Spacetimes
The possibility has been recently demonstrated to manufacture
(nonrelativistic, Hamiltonian) many-body problems which feature an isochronous
time evolution with an arbitrarily assigned period yet mimic with good
approximation, or even exactly, any given many-body problem (within a quite
large class, encompassing most of nonrelativistic physics) over times
which may also be arbitrarily large (but of course such that
). In this paper we review and further explore the possibility to
extend this finding to a general relativity context, so that it becomes
relevant for cosmology.Comment: Submitted to Acta Appl. Mat
Nonlinear stability of Minkowski spacetime in Nonlocal Gravity
We prove that the Minkowski spacetime is stable at nonlinear level and to all
perturbative orders in the gravitational perturbation in a general class of
nonlocal gravitational theories that are unitary and finite at quantum level
On the occurrence of gauge-dependent secularities in nonlinear gravitational waves
We study the plane (not necessarily monochromatic) gravitational waves at
nonlinear quadratic order on a flat background in vacuum. We show that, in the
harmonic gauge, the nonlinear waves are unstable. We argue that, at this order,
this instability can not be eliminated by means of a multiscale approach, i.e.
introducing suitable long variables, as it is often the case when secularities
appear in a perturbative scheme. However, this is a non-physical and
gauge-dependent effect that disappears in a suitable system of coordinates. In
facts, we show that in a specific gauge such instability does not occur, and
that it is possible to solve exactly the second order nonlinear equations of
gravitational waves. Incidentally, we note that this gauge coincides with the
one used by Belinski and Zakharov to find exact solitonic solutions of
Einstein's equations, that is to an exactly integrable case, and this fact
makes our second order nonlinear solutions less interesting. However, the
important warning is that one must be aware of the existence of the instability
reported in this paper, when studying nonlinear gravitational waves in the
harmonic gauge
Super-renormalizable or finite completion of the Starobinsky theory
The recent Planck data of Cosmic Microwave Background (CMB) temperature
anisotropies support the Starobinsky theory in which the quadratic Ricci scalar
drives cosmic inflation. We build up a multi-dimensional quantum consisted
ultraviolet completion of the model in a phenomenological "bottom-up approach".
We present the maximal class of theories compatible with unitarity and
(super-)renormalizability or finiteness which reduces to the Starobinsky theory
in the low-energy limit. The outcome is a maximal extension of the
Krasnikov-Tomboulis-Modesto theory including an extra scalar degree of freedom
besides the graviton field. The original theory was afterwards independently
discovered by Biswas-Gerwick-Koivisto-Mazumdar starting from first principles.
We explicitly show power counting super-renormalizability or finiteness (in odd
dimensions) and unitarity (no ghosts) of the theory. Any further extension of
the theory is non-unitary confirming the existence of at most one single extra
degree of freedom, the scalaron. A mechanism to achieve the Starobinsky theory
in string (field) theory is also investigated at the end of the paper.Comment: 12 pages, 1 figur
Non-unitarity of Minkowskian non-local quantum field theories
We show that Minkowskian non-local quantum field theories are not unitary. We
consider a simple one loop diagram for a scalar non-local field and show that
the imaginary part of the corresponding complex amplitude is not given by
Cutkosky rules, indeed this diagram violates the unitarity condition. We
compare this result with the case of an Euclidean non-local scalar field, that
has been shown to satisfy the Cutkosky rules, and we clearly identify the
reason of the breaking of unitarity of the Minkowskian theory
Cutkosky rules and perturbative unitarity in Euclidean nonlocal quantum field theories
We prove the unitarity of the Euclidean nonlocal scalar field theory to all
perturbative orders in the loop expansion. The amplitudes in the Euclidean
space are calculated assuming that all the particles have purely imaginary
energies, and afterwards they are analytically continued to real energies. We
show that such amplitudes satisfy the Cutkowsky rules and that only the cut
diagrams corresponding to normal thresholds contribute to their imaginary part.
This implies that the theory is unitary. This analysis is then exported to
nonlocal gauge and gravity theories by means of Becchi-Rouet-Stora-Tyutin or
diffeomorphism invariance, and Ward identities