1,524 research outputs found
Quantum Parabolic Sombrero
We have discussed the energy levels and probability distribution density for
a quantum particle placed in the two-dimensional sombrero-shaped potential
.Comment: 10 pages, LaTex, 6 figures (eps). accepted in Phys. Lett.
Quantum Systems with Hidden Symmetry. Interbasis Expansions
This monograph is the English version of the book "Quantum systems with
hidden symmetry. Interbasis expansions" published in 2006 by the publishing
house FIZMATLIT (Moscow) in Russian. When compiling this version of the book,
typos and inaccuracies noted since the release of the Russian edition have been
corrected
All-particle primary energy spectrum in the 3-200 PeV energy range
We present all-particle primary cosmic-ray energy spectrum in the 3-200 PeV
energy range obtained by a multi-parametric event-by-event evaluation of the
primary energy. The results are obtained on the basis of an expanded EAS data
set detected at mountain level (700 g/cm^2) by the GAMMA experiment. The energy
evaluation method has been developed using the EAS simulation with the SIBYLL
interaction model taking into account the response of GAMMA detectors and
reconstruction uncertainties of EAS parameters. Nearly unbiased (<5%) energy
estimations regardless of a primary nuclear mass with an accuracy of about
15-10% in the 3-200 PeV energy range respectively are attained. An irregularity
('bump') in the spectrum is observed at primary energies of ~74 PeV. This bump
exceeds a smooth power-law fit to the data by about 4 standard deviations. Not
rejecting stochastic nature of the bump completely, we examined the systematic
uncertainties of our methods and conclude that they cannot be responsible for
the observed feature.Comment: Accepted by J.Phys.G: Nucl.Part.Phy
Quantum oscillator as 1D anyon
It is shown that in one spatial dimension the quantum oscillator is dual to
the charged particle situated in the field described by the superposition of
Coulomb and Calogero-Sutherland potentials.Comment: 9 pages, LaTe
Second Hopf map and Yang-Coulomb system on 5d (pseudo)sphere
Using the second Hopf map, we perform the reduction of the eight-dimensional
(pseudo)spherical (Higgs)oscillator to a five-dimensional system interacting
with a Yang monopole. Then, using a standard trick, we obtain, from the latter
system, the pseudospherical and spherical generalizations of the Yang-Coulomb
system (the five dimensional analog of MICZ-Kepler system). We present the
whole set of its constants of motions, including the hidden symmetry generators
given by the analog of Runge-Lenz vector. In the same way, starting from the
eight-dimensional anisotropic inharmonic Higgs oscillator, we construct the
integrable (pseudo)spherical generalization of the Yang-Coulomb system with the
Stark term.Comment: 10 pages, PACS: 03.65.-w, 02.30.Ik, 14.80.H
3D Oscillator and Coulomb Systems reduced from Kahler spaces
We define the oscillator and Coulomb systems on four-dimensional spaces with
U(2)-invariant Kahler metric and perform their Hamiltonian reduction to the
three-dimensional oscillator and Coulomb systems specified by the presence of
Dirac monopoles. We find the Kahler spaces with conic singularity, where the
oscillator and Coulomb systems on three-dimensional sphere and two-sheet
hyperboloid are originated. Then we construct the superintegrable oscillator
system on three-dimensional sphere and hyperboloid, coupled to monopole, and
find their four-dimensional origins. In the latter case the metric of
configuration space is non-Kahler one. Finally, we extend these results to the
family of Kahler spaces with conic singularities.Comment: To the memory of Professor Valery Ter-Antonyan, 11 page
Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems
We propose the integrable (pseudo)spherical generalization of the
four-dimensional anisotropic oscillator with additional nonlinear potential.
Performing its Kustaanheimo-Stiefel transformation we then obtain the
pseudospherical generalization of the MICZ-Kepler system with linear and
potential terms. We also present the generalization of the
parabolic coordinates, in which this system admits the separation of variables.
Finally, we get the spherical analog of the presented MICZ-Kepler-like system.Comment: 7 page
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