Quantum groups, non-commutative Lorentzian spacetimes and curved momentum spaces

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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 $J=10^7 A/cm^2$, 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