1,438 research outputs found
Pitt's inequalities and uncertainty principle for generalized Fourier transform
We study the two-parameter family of unitary operators which are called
-generalized Fourier transforms and defined by the -deformed Dunkl
harmonic oscillator , , where
is the Dunkl Laplacian. Particular cases of such operators are the
Fourier and Dunkl transforms. The restriction of to radial
functions is given by the -deformed Hankel transform .
We obtain necessary and sufficient conditions for the weighted
Pitt inequalities to hold for the -deformed Hankel
transform. Moreover, we prove two-sided Boas--Sagher type estimates for the
general monotone functions. We also prove sharp Pitt's inequality for
transform in with the corresponding
weights. Finally, we establish the logarithmic uncertainty principle for
.Comment: 16 page
Fast and Robust Algorithm for the Energy Minimization of Spin Systems Applied in an Analysis of High Temperature Spin Configurations in Terms of Skyrmion Density
An algorithm for the minimization of the energy of magnetic systems is
presented and applied to the analysis of thermal configurations of a
ferromagnet to identify inherent structures, i.e. the nearest local energy
minima, as a function of temperature. Over a rather narrow temperature
interval, skyrmions appear and reach a high temperature limit for the skyrmion
density. In addition, the performance of the algorithm is further demonstrated
in a self-consistent field calculation of a skyrmion in an itinerant magnet.
The algorithm is based on a geometric approach in which the curvature of the
spherical domain is taken into account and as a result the length of the
magnetic moments is preserved in every iteration. In the limit of infinitesimal
rotations, the minimization path coincides with that obtained using damped spin
dynamics while the use of limited-memory quasi-newton minimization algorithms,
such as the limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm,
significantly accelerates the convergence
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