12,286 research outputs found
Orthogonality of Jack polynomials in superspace
Jack polynomials in superspace, orthogonal with respect to a
``combinatorial'' scalar product, are constructed. They are shown to coincide
with the Jack polynomials in superspace, orthogonal with respect to an
``analytical'' scalar product, introduced in hep-th/0209074 as eigenfunctions
of a supersymmetric quantum mechanical many-body problem. The results of this
article rely on generalizing (to include an extra parameter) the theory of
classical symmetric functions in superspace developed recently in
math.CO/0509408Comment: 22 pages, this supersedes the second part of math.CO/0412306; (v2) 24
pages, title and abstract slightly modified, minor changes, typos correcte
Singular polynomials for the rational Cherednik algebra for G(r,1,2)
We study the rational Cherednik algebra attached to the complex reflection
group . Each irreducible representation of
corresponds to a standard module for the rational Cherednik
algebra. We give necessary and sufficient conditions for the existence of
morphism between two of these modules and explicit formulas for them when they
exist
Higher harmonics of ac voltage response in narrow strips of YBa2Cu3O7 thin films: Evidence for strong thermal fluctuations
We report on measurements of higher harmonics of the ac voltage response in
strips of YBa2Cu3O7 thin films as a function of temperature, frequency and ac
current amplitude. The third (fifth) harmonic of the local voltage is found to
exhibit a negative (positive) peak at the superconducting transition
temperature and their amplitudes are closely related to the slope (derivative)
of the first (Ohmic) harmonic. The peaks practically do not depend on frequency
and no even (second or fourth) harmonics are detected. The observed data can be
interpreted in terms of ac current induced thermal modulation of the sample
temperature added to strong thermally activated fluctuations in the transition
region.Comment: 9 pages, 4 figures (PDF file
Classical symmetric functions in superspace
We present the basic elements of a generalization of symmetric function
theory involving functions of commuting and anticommuting (Grassmannian)
variables. These new functions, called symmetric functions in superspace, are
invariant under the diagonal action of the symmetric group on the sets of
commuting and anticommuting variables. In this work, we present the superspace
extension of the classical bases, namely, the monomial symmetric functions, the
elementary symmetric functions, the completely symmetric functions, and the
power sums. Various basic results, such as the generating functions for the
multiplicative bases, Cauchy formulas, involution operations as well as the
combinatorial scalar product are also generalized.Comment: 21 pages, this supersedes the first part of math.CO/041230
Thermodynamics of a BTZ black hole solution with an Horndeski source
In three dimensions, we consider a particular truncation of the Horndeski
action that reduces to the Einstein-Hilbert Lagrangian with a cosmological
constant and a scalar field whose dynamics is governed by its usual
kinetic term together with a nonminimal kinetic coupling. Requiring the radial
component of the conserved current to vanish, the solution turns out to be the
BTZ black hole geometry with a radial scalar field well-defined at the horizon.
This means in particular that the stress tensor associated to the matter source
behaves on-shell as an effective cosmological constant term. We construct an
Euclidean action whose field equations are consistent with the original ones
and such that the constraint on the radial component of the conserved current
also appears as a field equation. With the help of this Euclidean action, we
derive the mass and the entropy of the solution, and found that they are
proportional to the thermodynamical quantities of the BTZ solution by an
overall factor that depends on the cosmological constant. The reality condition
and the positivity of the mass impose the cosmological constant to be bounded
from above as where the limiting case
reduces to the BTZ solution with a vanishing scalar
field. Exploiting a scaling symmetry of the reduced action, we also obtain the
usual three-dimensional Smarr formula. In the last section, we extend all these
results in higher dimensions where the metric turns out to be the
Schwarzschild-AdS spacetime with planar horizon.Comment: 7 page
Generalized Hermite polynomials in superspace as eigenfunctions of the supersymmetric rational CMS model
We present an algebraic construction of the orthogonal eigenfunctions of the
supersymmetric extension of the rational Calogero-Moser-Sutherland model with
harmonic confinement. These eigenfunctions are the superspace extension of the
generalized Hermite (or Hi-Jack) polynomials. The conserved quantities of the
rational supersymmetric model are related to their trigonometric relatives
through a similarity transformation. This leads to a simple expression between
the corresponding eigenfunctions: the generalized Hermite superpolynomials are
written as a differential operator acting on the corresponding Jack
superpolynomials. As an aside, the maximal superintegrability of the
supersymmetric rational Calogero-Moser-Sutherland model is demonstrated.Comment: Latex 2e, shortened version, one reference added, 18 page
Jack superpolynomials: physical and combinatorial definitions
Jack superpolynomials are eigenfunctions of the supersymmetric extension of
the quantum trigonometric Calogero-Moser-Sutherland. They are orthogonal with
respect to the scalar product, dubbed physical, that is naturally induced by
this quantum-mechanical problem. But Jack superpolynomials can also be defined
more combinatorially, starting from the multiplicative bases of symmetric
superpolynomials, enforcing orthogonality with respect to a one-parameter
deformation of the combinatorial scalar product. Both constructions turns out
to be equivalent. This provides strong support for the correctness of the
various underlying constructions and for the pivotal role of Jack
superpolynomials in the theory of symmetric superpolynomials.Comment: 6 pages. To appear in the proceedings of the {\it XIII International
Colloquium on Integrable Systems and Quantum Groups}, Czech. J . Phys., June
17-19 2004, Doppler Institute, Czech Technical Universit
Higher-dimensional black holes with a conformally invariant Maxwell source
We consider an action for an abelian gauge field for which the density is
given by a power of the Maxwell Lagrangian. In d spacetime dimensions this
action is shown to enjoy the conformal invariance if the power is chosen as
d/4. We take advantage of this conformal invariance to derive black hole
solutions electrically charged with a purely radial electric field. Because of
considering power of the Maxwell density, the black hole solutions exist only
for dimensions which are multiples of four. The expression of the electric
field does not depend on the dimension and corresponds to the four-dimensional
Reissner-Nordstrom field. Using the Hamiltonian action we identify the mass and
the electric charge of these black hole solutions.Comment: 5 page
Vortex pinning in high-Tc materials via randomly oriented columnar defects, created by GeV proton-induced fission fragments
Extensive work has shown that irradiation with 0.8 GeV protons can produce
randomly oriented columnar defects (CD's) in a large number of HTS materials,
specifically those cuprates containing Hg, Tl, Pb, Bi, and similar heavy
elements. Absorbing the incident proton causes the nucleus of these species to
fission, and the recoiling fission fragments create amorphous tracks, i.e.,
CD's. The superconductive transition temperature Tc decreases linearly with
proton fluence and we analyze how the rate depends on the family of
superconductors. In a study of Tl-2212 materials, adding defects decreases the
equilibrium magnetization Meq(H) significantly in magnitude and changes its
field dependence; this result is modeled in terms of vortex pinning. Analysis
of the irreversible magnetization and its time dependence shows marked
increases in the persistent current density and effective pinning energy, and
leads to an estimate for the elementary attempt time for vortex hopping, tau ~
4x10^(-9) s.Comment: Submitted to Physica C; presentation at ISS-2001. PDF file only, 13
pp. tota
Monotone traveling wavefronts of the KPP-Fisher delayed equation
In the early 2000's, Gourley (2000), Wu et al. (2001), Ashwin et al. (2002)
initiated the study of the positive wavefronts in the delayed
Kolmogorov-Petrovskii-Piskunov-Fisher equation. Since then, this model has
become one of the most popular objects in the studies of traveling waves for
the monostable delayed reaction-diffusion equations. In this paper, we give a
complete solution to the problem of existence and uniqueness of monotone waves
in the KPP-Fisher equation. We show that each monotone traveling wave can be
found via an iteration procedure. The proposed approach is based on the use of
special monotone integral operators (which are different from the usual Wu-Zou
operator) and appropriate upper and lower solutions associated to them. The
analysis of the asymptotic expansions of the eventual traveling fronts at
infinity is another key ingredient of our approach.Comment: 25 pages, 2 figures, submitte
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