2,670 research outputs found
Cooper pair dispersion relation in two dimensions
The Cooper pair binding energy {\it vs.} center-of-mass-momentum dispersion
relation for Bose-Einstein condensation studies of superconductivity is found
in two dimensions for a renormalized attractive delta interaction. It crosses
over smoothly from a linear to a quadratic form as coupling varies from weak to
strong.Comment: 2 pages, 1 figure, new version published in Physica
Constraint-preserving boundary conditions in the 3+1 first-order approach
A set of energy-momentum constraint-preserving boundary conditions is
proposed for the first-order Z4 case. The stability of a simple numerical
implementation is tested in the linear regime (robust stability test), both
with the standard corner and vertex treatment and with a modified
finite-differences stencil for boundary points which avoids corners and
vertices even in cartesian-like grids. Moreover, the proposed boundary
conditions are tested in a strong field scenario, the Gowdy waves metric,
showing the expected rate of convergence. The accumulated amount of
energy-momentum constraint violations is similar or even smaller than the one
generated by either periodic or reflection conditions, which are exact in the
Gowdy waves case. As a side theoretical result, a new symmetrizer is explicitly
given, which extends the parametric domain of symmetric hyperbolicity for the
Z4 formalism. The application of these results to first-order BSSN-like
formalisms is also considered.Comment: Revised version, with conclusive numerical evidence. 23 pages, 12
figure
Bose-Einstein condensation of nonzero-center-of-mass-momentum Cooper pairs
Cooper pair (CP) binding with both zero and nonzero center-of-mass momenta
(CMM) is studied with a set of renormalized equations assuming a short-ranged
(attractive) pairwise interfermion interaction. Expanding the associated
dispersion relation in 2D in powers of the CMM, in weak-to-moderate coupling a
term {\it linear} in the CMM dominates the pair excitation energy, while the
quadratic behavior usually assumed in Bose-Einstein (BE)-condensation studies
prevails for any coupling {\it only} in the limit of zero Fermi velocity when
the Fermi sea disappears, i.e., in vacuum. In 3D this same behavior is observed
numerically. The linear term, moreover, exhibits CP breakup beyond a threshold
CMM value which vanishes with coupling. This makes all the excited
(nonzero-CMM) BE levels with preformed CPs collapse into a single ground level
so that a BCS condensate (where only zero CMM CPs are usually allowed) appears
in zero coupling to be a special case in either 2D or 3D of the BE condensate
of linear-dispersion-relation CPs.Comment: Four pages including four figures. To be published in Physica
Bayesian approach and Naturalness in MSSM analyses for the LHC
The start of LHC has motivated an effort to determine the relative
probability of the different regions of the MSSM parameter space, taking into
account the present, theoretical and experimental, wisdom about the model.
Since the present experimental data are not powerful enough to select a small
region of the MSSM parameter space, the choice of a judicious prior probability
for the parameters becomes most relevant. Previous studies have proposed
theoretical priors that incorporate some (conventional) measure of the
fine-tuning, to penalize unnatural possibilities. However, we show that such
penalization arises from the Bayesian analysis itself (with no ad hoc
assumptions), upon the marginalization of the mu-parameter. Furthermore the
resulting effective prior contains precisely the Barbieri-Giudice measure,
which is very satisfactory. On the other hand we carry on a rigorous treatment
of the Yukawa couplings, showing in particular that the usual practice of
taking the Yukawas "as required", approximately corresponds to taking
logarithmically flat priors in the Yukawa couplings. Finally, we use an
efficient set of variables to scan the MSSM parameter space, trading in
particular B by tan beta, giving the effective prior in the new parameters.
Beside the numerical results, we give accurate analytic expressions for the
effective priors in all cases. Whatever experimental information one may use in
the future, it is to be weighted by the Bayesian factors worked out here.Comment: LaTeX, 19 pages, 3 figure
Linear to quadratic crossover of Cooper pair dispersion relation
Cooper pairing is studied in three dimensions to determine its binding energy
for all coupling using a general separable interfermion interaction. Also
considered are Cooper pairs (CPs) with nonzero center-of-mass momentum (CMM). A
coupling-independent {\it linear} term in the CMM dominates the pair excitation
energy in weak coupling and/or high fermion density, while the more familiar
quadratic term prevails only in the extreme low-density (i.e., vacuum) limit
for any nonzero coupling. The linear-to-quadratic crossover of the CP
dispersion relation is analyzed numerically, and is expected to play a central
role in a model of superconductivity (and superfluidity) simultaneously
accommodating a BCS condensate as well as a Bose-Einstein condensate of CP
bosons.Comment: 13 pages plus 2 figure
Towards a gauge-polyvalent Numerical Relativity code
The gauge polyvalence of a new numerical code is tested, both in
harmonic-coordinate simulations (gauge-waves testbed) and in
singularity-avoiding coordinates (simple Black-Hole simulations, either with or
without shift). The code is built upon an adjusted first-order
flux-conservative version of the Z4 formalism and a recently proposed family of
robust finite-difference high-resolution algorithms. An outstanding result is
the long-term evolution (up to 1000M) of a Black-Hole in normal coordinates
(zero shift) without excision.Comment: to appear in Physical Review
Finite element approximation of sparse parabolic control problems
We study the finite element approximation of an optimal control problem governed by a semilinear partial differential equation and whose objective function includes a term promoting space sparsity of the solutions. We prove existence of solution in the absence of control bound constraints and provide the adequate second order sufficient conditions to obtain error estimates. Full discretization of the problem is carried out, and the sparsity properties of the discrete solutions, as well as error estimates, are obtained.The first two authors were partially supported by the Spanish Ministerio de Economía y Competitividad under project MTM2014-57531-P
Time-varying coefficient estimation in SURE models. Application to portfolio management.
This paper provides a detailed analysis of the asymptotic properties of a kernel estimator for a Seemingly Unrelated Regression Equations model with time-varying coefficients (tv-SURE) under very general conditions. Theoretical results together with a simulation study differentiates the cases for which the estimation of a tv-SURE outperforms the estimation of a Single Regression Equations model with time-varying coefficients (tv-SRE). The study shows that Zellner's results cannot be straightforwardly extended to the time-varying case. The tv-SURE is applied to the Fama and French five-factor model using data from four different international markets. Finally, we provide the estimation under cross-restriction and discuss a testing procedure
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