871 research outputs found
Two-band superconductors: Extended Ginzburg-Landau formalism by a systematic expansion in small deviation from the critical temperature
We derive the extended Ginzburg-Landau (GL) formalism for a clean s-wave
two-band superconductor by employing a systematic expansion of the free-energy
functional and the corresponding matrix gap equation in powers of the small
deviation from the critical temperature tau = 1-T/T_c. The two lowest orders of
this expansion produce the equation for T_c and the GL theory. It is shown that
in agreement with previous studies, the two-band GL theory maps onto the
single-band GL model and thus fails to describe the difference in the spatial
profiles of the two band condensates. We prove that except for some very
special cases, this difference appears already in the leading correction to the
GL theory, which constitutes the extended GL formalism. We derive linear
differential equations that determine the leading corrections to the band order
parameters and magnetic field, discuss the validity of these equations, and
consider examples of an important interplay between the band condensates.
Finally, we present numerical results for the thermodynamic critical magnetic
field and temperature-dependent band gaps (at zero field), which are in a very
good agreement with those obtained from the full BCS approach in a wide
temperature range. To this end, we emphasize the advantages of our extended GL
theory in comparison with the often used two-component GL-like model based on
an unreconstructed two-band generalization of the Gor'kov derivation
Limits on non-Gaussianities from WMAP data
We develop a method to constrain the level of non-Gaussianity of density
perturbations when the 3-point function is of the "equilateral" type.
Departures from Gaussianity of this form are produced by single field models
such as ghost or DBI inflation and in general by the presence of higher order
derivative operators in the effective Lagrangian of the inflaton. We show that
the induced shape of the 3-point function can be very well approximated by a
factorizable form, making the analysis practical. We also show that, unless one
has a full sky map with uniform noise, in order to saturate the Cramer-Rao
bound for the error on the amplitude of the 3-point function, the estimator
must contain a piece that is linear in the data. We apply our technique to the
WMAP data obtaining a constraint on the amplitude f_NL^equil of "equilateral"
non-Gaussianity: -366 < f_NL^equil < 238 at 95% C.L. We also apply our
technique to constrain the so-called "local" shape, which is predicted for
example by the curvaton and variable decay width models. We show that the
inclusion of the linear piece in the estimator improves the constraint over
those obtained by the WMAP team, to -27 < f_NL^local < 121 at 95% C.L.Comment: 20 pages, 12 eps figure
Can billiard eigenstates be approximated by superpositions of plane waves?
The plane wave decomposition method (PWDM) is one of the most popular
strategies for numerical solution of the quantum billiard problem. The method
is based on the assumption that each eigenstate in a billiard can be
approximated by a superposition of plane waves at a given energy. By the
classical results on the theory of differential operators this can indeed be
justified for billiards in convex domains. On the contrary, in the present work
we demonstrate that eigenstates of non-convex billiards, in general, cannot be
approximated by any solution of the Helmholtz equation regular everywhere in
(in particular, by linear combinations of a finite number of plane waves
having the same energy). From this we infer that PWDM cannot be applied to
billiards in non-convex domains. Furthermore, it follows from our results that
unlike the properties of integrable billiards, where each eigenstate can be
extended into the billiard exterior as a regular solution of the Helmholtz
equation, the eigenstates of non-convex billiards, in general, do not admit
such an extension.Comment: 23 pages, 5 figure
Probing local non-Gaussianities within a Bayesian framework
Aims: We outline the Bayesian approach to inferring f_NL, the level of
non-Gaussianity of local type. Phrasing f_NL inference in a Bayesian framework
takes advantage of existing techniques to account for instrumental effects and
foreground contamination in CMB data and takes into account uncertainties in
the cosmological parameters in an unambiguous way.
Methods: We derive closed form expressions for the joint posterior of f_NL
and the reconstructed underlying curvature perturbation, Phi, and deduce the
conditional probability densities for f_NL and Phi. Completing the inference
problem amounts to finding the marginal density for f_NL. For realistic data
sets the necessary integrations are intractable. We propose an exact
Hamiltonian sampling algorithm to generate correlated samples from the f_NL
posterior. For sufficiently high signal-to-noise ratios, we can exploit the
assumption of weak non-Gaussianity to find a direct Monte Carlo technique to
generate independent samples from the posterior distribution for f_NL. We
illustrate our approach using a simplified toy model of CMB data for the simple
case of a 1-D sky.
Results: When applied to our toy problem, we find that, in the limit of high
signal-to-noise, the sampling efficiency of the approximate algorithm
outperforms that of Hamiltonian sampling by two orders of magnitude. When f_NL
is not significantly constrained by the data, the more efficient, approximate
algorithm biases the posterior density towards f_NL = 0.Comment: 11 pages, 7 figures. Accepted for publication in Astronomy and
Astrophysic
Exact Solution for the Critical State in Thin Superconductor Strips with Field Dependent or Anisotropic Pinning
An exact analytical solution is given for the critical state problem in long
thin superconductor strips in a perpendicular magnetic field, when the critical
current density j_c(B) depends on the local induction B according to a simple
three-parameter model. This model describes both isotropic superconductors with
this j_c(B) dependence, but also superconductors with anisotropic pinning
described by a dependence j_c(theta) where theta is the tilt angle of the flux
lines away from the normal to the specimen plane
Phonon-Coupled Electron Tunneling in Two and Three-Dimensional Tunneling Configurations
We treat a tunneling electron coupled to acoustical phonons through a
realistic electron phonon interaction: deformation potential and piezoelectric,
in two or three-dimensional tunneling configurations. Making use of slowness of
the phonon system compared to electron tunneling, and using a Green function
method for imaginary time, we are able to calculate the change in the
transition probability due to the coupling to phonons. It is shown using
standard renormalization procedure that, contrary to the one-dimensional case,
second order perturbation theory is sufficient in order to treat the
deformation potential coupling, which leads to a small correction to the
transmission coefficient prefactor. In the case of piezoelectric coupling,
which is found to be closely related to the piezoelectric polaron problem,
vertex corrections need to be considered. Summing leading logarithmic terms, we
show that the piezoelectric coupling leads to a significant change of the
transmission coefficient.Comment: 17 pages, 4 figure
An Improved Calculation of the Non-Gaussian Halo Mass Function
The abundance of collapsed objects in the universe, or halo mass function, is
an important theoretical tool in studying the effects of primordially generated
non-Gaussianities on the large scale structure. The non-Gaussian mass function
has been calculated by several authors in different ways, typically by
exploiting the smallness of certain parameters which naturally appear in the
calculation, to set up a perturbative expansion. We improve upon the existing
results for the mass function by combining path integral methods and saddle
point techniques (which have been separately applied in previous approaches).
Additionally, we carefully account for the various scale dependent combinations
of small parameters which appear. Some of these combinations in fact become of
order unity for large mass scales and at high redshifts, and must therefore be
treated non-perturbatively. Our approach allows us to do this, and to also
account for multi-scale density correlations which appear in the calculation.
We thus derive an accurate expression for the mass function which is based on
approximations that are valid over a larger range of mass scales and redshifts
than those of other authors. By tracking the terms ignored in the analysis, we
estimate theoretical errors for our result and also for the results of others.
We also discuss the complications introduced by the choice of smoothing filter
function, which we take to be a top-hat in real space, and which leads to the
dominant errors in our expression. Finally, we present a detailed comparison
between the various expressions for the mass functions, exploring the accuracy
and range of validity of each.Comment: 28 pages, 13 figures; v2: text reorganized and some figured modified
for clarity, results unchanged, references added. Matches version published
in JCA
Critical State in Thin Anisotropic Superconductors of Arbitrary Shape
A thin flat superconductor of arbitrary shape and with arbitrary in-plane and
out-of-plane anisotropy of flux-line pinning is considered, in an external
magnetic field normal to its plane.
It is shown that the general three-dimensional critical state problem for
this superconductor reduces to the two-dimensional problem of an infinitely
thin sample of the same shape but with a modified induction dependence of the
critical sheet current. The methods of solving the latter problem are well
known. This finding thus enables one to study the critical states in realistic
samples of high-Tc superconductors with various types of anisotropic flux-line
pinning. As examples, we investigate the critical states of long strips and
rectangular platelets of high-Tc superconductors with pinning either by the
ab-planes or by extended defects aligned with the c-axis.Comment: 13 pages including 13 figure files in the tex
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