14,671 research outputs found
Detecting photon-photon scattering in vacuum at exawatt lasers
In a recent paper, we have shown that the QED nonlinear corrections imply a
phase correction to the linear evolution of crossing electromagnetic waves in
vacuum. Here, we provide a more complete analysis, including a full numerical
solution of the QED nonlinear wave equations for short-distance propagation in
a symmetric configuration. The excellent agreement of such a solution with the
result that we obtain using our perturbatively-motivated Variational Approach
is then used to justify an analytical approximation that can be applied in a
more general case. This allows us to find the most promising configuration for
the search of photon-photon scattering in optics experiments. In particular, we
show that our previous requirement of phase coherence between the two crossing
beams can be released. We then propose a very simple experiment that can be
performed at future exawatt laser facilities, such as ELI, by bombarding a low
power laser beam with the exawatt bump.Comment: 8 pages, 6 figure
The connected components of the space of Alexandrov surfaces
Denote by the set of all compact Alexandrov surfaces
with curvature bounded below by without boundary, endowed with the
topology induced by the Gromov-Hausdorff metric. We determine the connected
components of and of its closure
Optical measurements of spin noise as a high resolution spectroscopic tool
The intrinsic fluctuations of electron spins in semiconductors and atomic
vapors generate a small, randomly-varying "spin noise" that can be detected by
sensitive optical methods such as Faraday rotation. Recent studies have
demonstrated that the frequency, linewidth, and lineshape of this spin noise
directly reveals dynamical spin properties such as dephasing times, relaxation
mechanisms and g-factors without perturbing the spins away from equilibrium.
Here we demonstrate that spin noise measurements using wavelength-tunable probe
light forms the basis of a powerful and novel spectroscopic tool to provide
unique information that is fundamentally inaccessible via conventional linear
optics. In particular, the wavelength dependence of the detected spin noise
power can reveal homogeneous linewidths buried within inhomogeneously-broadened
optical spectra, and can resolve overlapping optical transitions belonging to
different spin systems. These new possibilities are explored both theoretically
and via experiments on spin systems in opposite limits of inhomogeneous
broadening (alkali atom vapors and semiconductor quantum dots).Comment: 4 pages, 4 figure
Performance of the modified Becke-Johnson potential
Very recently, in the 2011 version of the Wien2K code, the long standing
shortcome of the codes based on Density Functional Theory, namely, its
impossibility to account for the experimental band gap value of semiconductors,
was overcome. The novelty is the introduction of a new exchange and correlation
potential, the modified Becke-Johnson potential (mBJLDA). In this paper, we
report our detailed analysis of this recent work. We calculated using this
code, the band structure of forty one semiconductors and found an important
improvement in the overall agreement with experiment as Tran and Blaha [{\em
Phys. Rev. Lett.} 102, 226401 (2009)] did before for a more reduced set of
semiconductors. We find, nevertheless, within this enhanced set, that the
deviation from the experimental gap value can reach even much more than 20%, in
some cases. Furthermore, since there is no exchange and correlation energy term
from which the mBJLDA potential can be deduced, a direct optimization procedure
to get the lattice parameter in a consistent way is not possible as in the
usual theory. These authors suggest that a LDA or a GGA optimization procedure
is used previous to a band structure calculation and the resulting lattice
parameter introduced into the 2011 code. This choice is important since small
percentage differences in the lattice parameter can give rise to quite higher
percentage deviations from experiment in the predicted band gap value.Comment: 10 pages, 2 figures, 5 Table
Characterizing normal crossing hypersurfaces
The objective of this article is to give an effective algebraic
characterization of normal crossing hypersurfaces in complex manifolds. It is
shown that a hypersurface has normal crossings if and only if it is a free
divisor, has a radical Jacobian ideal and a smooth normalization. Using K.
Saito's theory of free divisors, also a characterization in terms of
logarithmic differential forms and vector fields is found and and finally
another one in terms of the logarithmic residue using recent results of M.
Granger and M. Schulze.Comment: v2: typos fixed, final version to appear in Math. Ann.; 24 pages, 2
figure
- …