2,903 research outputs found
B polarization of the CMB from Faraday rotation
We study the effect of Faraday rotation due to a homogeneous magnetic field
on the polarization of the cosmic microwave background (CMB). Scalar
fluctuations give rise only to parity-even E-type polarization of the CMB.
However in the presence of a magnetic field, a non-vanishing parity-odd B-type
polarization component is produced through Faraday rotation. We derive the
exact solution for the E and B modes generated by scalar perturbations
including the Faraday rotation effect of a uniform magnetic field, and evaluate
their cross-correlations with temperature anisotropies. We compute the angular
autocorrelation function of the B-modes in the limit that the Faraday rotation
is small. We find that primordial magnetic fields of present strength around
G rotate E-modes into B-modes with amplitude comparable to those
due to the weak gravitational lensing effect at frequencies around
GHz. The strength of B-modes produced by Faraday rotation scales as
. We evaluate also the depolarizing effect of Faraday rotation upon
the cross correlation between temperature anisotropy and E-type polarization.Comment: 11 pages, 4 figures. Minor changes to match the published versio
Correlations, fluctuations and stability of a finite-size network of coupled oscillators
The incoherent state of the Kuramoto model of coupled oscillators exhibits
marginal modes in mean field theory. We demonstrate that corrections due to
finite size effects render these modes stable in the subcritical case, i.e.
when the population is not synchronous. This demonstration is facilitated by
the construction of a non-equilibrium statistical field theoretic formulation
of a generic model of coupled oscillators. This theory is consistent with
previous results. In the all-to-all case, the fluctuations in this theory are
due completely to finite size corrections, which can be calculated in an
expansion in 1/N, where N is the number of oscillators. The N -> infinity limit
of this theory is what is traditionally called mean field theory for the
Kuramoto model.Comment: 25 pages (2 column), 12 figures, modifications for resubmissio
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