445,156 research outputs found
Parallel integer relation detection: techniques and applications
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Supersymmetric Quantum Mechanics and Painlev\'e IV Equation
As it has been proven, the determination of general one-dimensional
Schr\"odinger Hamiltonians having third-order differential ladder operators
requires to solve the Painlev\'e IV equation. In this work, it will be shown
that some specific subsets of the higher-order supersymmetric partners of the
harmonic oscillator possess third-order differential ladder operators. This
allows us to introduce a simple technique for generating solutions of the
Painlev\'e IV equation. Finally, we classify these solutions into three
relevant hierarchies.Comment: Proceedings of the Workshop 'Supersymmetric Quantum Mechanics and
Spectral Design' (July 18-30, 2010, Benasque, Spain
Complex solutions to Painleve IV equation through supersymmetric quantum mechanics
In this work, supersymmetric quantum mechanics will be used to obtain complex
solutions to Painleve IV equation with real parameters. We will also focus on
the properties of the associated Hamiltonians, i.e. the algebraic structure,
the eigenfunctions and the energy spectra.Comment: 5 pages, 3 figures. Talk given at the Advanced Summer School 2011,
Cinvestav (Mexico City), July 201
Selected Legal and Poicy Trends in Takings Law: Background Principles, Custom and Public Trust Exceptions and the (Mis)use of Investment-Backed Expectations
Supersymmetric quantum mechanics and Painleve equations
In these lecture notes we shall study first the supersymmetric quantum
mechanics (SUSY QM), specially when applied to the harmonic and radial
oscillators. In addition, we will define the polynomial Heisenberg algebras
(PHA), and we will study the general systems ruled by them: for zero and first
order we obtain the harmonic and radial oscillators, respectively; for second
and third order PHA the potential is determined by solutions to Painleve IV
(PIV) and Painleve V (PV) equations. Taking advantage of this connection, later
on we will find solutions to PIV and PV equations expressed in terms of
confluent hypergeometric functions. Furthermore, we will classify them into
several solution hierarchies, according to the specific special functions they
are connected with.Comment: 38 pages, 20 figures. Lecture presented at the XLIII Latin American
School of Physics: ELAF 2013 in Mexico Cit
High field magnetotransport in composite conductors: the effective medium approximation revisited
The self consistent effective medium approximation (SEMA) is used to study
three-dimensional random conducting composites under the influence of a strong
magnetic field {\bf B}, in the case where all constituents exhibit isotropic
response. Asymptotic analysis is used to obtain almost closed form results for
the strong field magnetoresistance and Hall resistance in various types of two-
and three-constituent isotropic mixtures for the entire range of compositions.
Numerical solutions of the SEMA equations are also obtained, in some cases, and
compared with those results. In two-constituent
free-electron-metal/perfect-insulator mixtures, the magnetoresistance is
asymptotically proportional to at {\em all concentrations above the
percolation threshold}. In three-constituent metal/insulator/superconductor
mixtures a line of critical points is found, where the strong field
magnetoresistance switches abruptly from saturating to non-saturating
dependence on , at a certain value of the
insulator-to-superconductor concentration ratio. This transition appears to be
related to the phenomenon of anisotropic percolation.Comment: 16 pages, 3 figure
Galaxy-Galaxy Flexion: Weak Lensing to Second Order
In this paper, we develop a new gravitational lensing inversion technique.
While traditional approaches assume that the lensing field varies little across
a galaxy image, we note that this variation in the field can give rise to a
``Flexion'' or bending of a galaxy image, which may then be used to detect a
lensing signal with increased signal to noise. Since the significance of the
Flexion signal increases on small scales, this is ideally suited to
galaxy-galaxy lensing. We develop an inversion technique based on the
``Shapelets'' formalism of Refregier (2003). We then demonstrate the proof of
this concept by measuring a Flexion signal in the Deep Lens Survey. Assuming an
intrinsically isothermal distribution, we find from the Flexion signal alone a
velocity width of v_c=221\pm 12 km/s for lens galaxies of r < 21.5, subject to
uncertainties in the intrinsic Flexion distribution.Comment: 11 pages, Latex, 4 figures. Accepted by ApJ, changes include revision
of errors from previous draf
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