2,285 research outputs found
Superintegrability on sl(2)-coalgebra spaces
We review a recently introduced set of N-dimensional quasi-maximally
superintegrable Hamiltonian systems describing geodesic motions, that can be
used to generate "dynamically" a large family of curved spaces. From an
algebraic viewpoint, such spaces are obtained through kinetic energy
Hamiltonians defined on either the sl(2) Poisson coalgebra or a quantum
deformation of it. Certain potentials on these spaces and endowed with the same
underlying coalgebra symmetry have been also introduced in such a way that the
superintegrability properties of the full system are preserved. Several new N=2
examples of this construction are explicitly given, and specific Hamiltonians
leading to spaces of non-constant curvature are emphasized.Comment: 12 pages. Based on the contribution presented at the "XII
International Conference on Symmetry Methods in Physics", Yerevan (Armenia),
July 2006. To appear in Physics of Atomic Nucle
Superintegrability on N-dimensional spaces of constant curvature from so(N+1) and its contractions
The Lie-Poisson algebra so(N+1) and some of its contractions are used to
construct a family of superintegrable Hamiltonians on the ND spherical,
Euclidean, hyperbolic, Minkowskian and (anti-)de Sitter spaces. We firstly
present a Hamiltonian which is a superposition of an arbitrary central
potential with N arbitrary centrifugal terms. Such a system is quasi-maximally
superintegrable since this is endowed with 2N-3 functionally independent
constants of the motion (plus the Hamiltonian). Secondly, we identify two
maximally superintegrable Hamiltonians by choosing a specific central potential
and finding at the same time the remaining integral. The former is the
generalization of the Smorodinsky-Winternitz system to the above six spaces,
while the latter is a generalization of the Kepler-Coulomb potential, for which
the Laplace-Runge-Lenz N-vector is also given. All the systems and constants of
the motion are explicitly expressed in a unified form in terms of ambient and
polar coordinates as they are parametrized by two contraction parameters
(curvature and signature of the metric).Comment: 14 pages. Based on the contribution presented at the "XII
International Conference on Symmetry Methods in Physics", Yerevan (Armenia),
July 2006. To appear in Physics of Atomic Nucle
Integrable potentials on spaces with curvature from quantum groups
A family of classical integrable systems defined on a deformation of the
two-dimensional sphere, hyperbolic and (anti-)de Sitter spaces is constructed
through Hamiltonians defined on the non-standard quantum deformation of a sl(2)
Poisson coalgebra. All these spaces have a non-constant curvature that depends
on the deformation parameter z. As particular cases, the analogues of the
harmonic oscillator and Kepler--Coulomb potentials on such spaces are proposed.
Another deformed Hamiltonian is also shown to provide superintegrable systems
on the usual sphere, hyperbolic and (anti-)de Sitter spaces with a constant
curvature that exactly coincides with z. According to each specific space, the
resulting potential is interpreted as the superposition of a central harmonic
oscillator with either two more oscillators or centrifugal barriers. The
non-deformed limit z=0 of all these Hamiltonians can then be regarded as the
zero-curvature limit (contraction) which leads to the corresponding
(super)integrable systems on the flat Euclidean and Minkowskian spaces.Comment: 19 pages, 1 figure. Two references adde
Detection of spin torque magnetization dynamics through low frequency noise
We present a comparative study of high frequency dynamics and low frequency
noise in elliptical magnetic tunnel junctions with lateral dimensions under 100
nm presenting current-switching phenomena. The analysis of the high frequency
oscillation modes with respect to the current reveals the onset of a
steady-state precession regime for negative bias currents above , when the magnetic field is applied along the easy axis of
magnetization. By the study of low frequency noise for the same samples, we
demonstrate the direct link between changes in the oscillation modes with the
applied current and the normalised low frequency (1/f) noise as a function of
the bias current. These findings prove that low frequency noise studies could
be a simple and powerful technique to investigate spin-torque based
magnetization dynamics
Low frequency noise due to magnetic inhomogeneities in submicron FeCoB/MgO/FeCoB magnetic tunnel junctions
We report on room temperature low frequency noise due to magnetic
inhomogeneities/domain walls (MI/DWs) in elliptic submicron FeCoB/MgO/FeCoB
magnetic tunnel junctions with an area between 0.0245 and 0.0675{\mu}m2. In the
smaller area junctions we found an unexpected random telegraph noise (RTN1),
deeply in the parallel state, possibly due to stray field induced MI/DWs in the
hard layer. The second noise source (RTN2) is observed in the antiparallel
state for the largest junctions. Strong asymmetry of RTN2 and of related
resistance steps with current indicate spin torque acting on the MI/DWs in the
soft layer at current densities below 5x10^5 A/cm2.Comment: 12 pages, 4 figure
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