3,312 research outputs found
Multi-center MICZ-Kepler systems
We present the classical solutions of the two-center MICZ-Kepler and
MICZ-Kepler-Stark systems. Then we suggest the model of multi-center
MICZ-Kepler system on the curved spaces equipped with -invariant
conformal flat metrics.Comment: 7 pages, typos corrected, refs added. Contribution to the Proceedings
of International Workshop on Classical and Quantum Integrable systems,
24-28.01.2007, Dubna, Russi
Phase Transition in a One-Dimensional Extended Peierls-Hubbard Model with a Pulse of Oscillating Electric Field: III. Interference Caused by a Double Pulse
In order to study consequences of the differences between the
ionic-to-neutral and neutral-to-ionic transitions in the one-dimensional
extended Peierls-Hubbard model with alternating potentials for the TTF-CA
complex, we introduce a double pulse of oscillating electric field in the
time-dependent Schr\"odinger equation and vary the interval between the two
pulses as well as their strengths. When the dimerized ionic phase is
photoexcited, the interference effect is clearly observed owing to the
coherence of charge density and lattice displacements. Namely, the two pulses
constructively interfere with each other if the interval is a multiple of the
period of the optical lattice vibration, while they destructively interfere if
the interval is a half-odd integer times the period, in the processes toward
the neutral phase. The interference is strong especially when the pulse is
strong and short because the coherence is also strong. Meanwhile, when the
neutral phase is photoexcited, the interference effect is almost invisible or
weakly observed when the pulse is weak. The photoinduced lattice oscillations
are incoherent due to random phases. The strength of the interference caused by
a double pulse is a key quantity to distinguish the two transitions and to
evaluate the coherence of charge density and lattice displacements.Comment: 16 pages, 8 figure
A Generalization of the Kepler Problem
We construct and analyze a generalization of the Kepler problem. These
generalized Kepler problems are parameterized by a triple
where the dimension is an integer, the curvature is a real
number, the magnetic charge is a half integer if is odd and is 0 or
1/2 if is even. The key to construct these generalized Kepler problems is
the observation that the Young powers of the fundamental spinors on a punctured
space with cylindrical metric are the right analogues of the Dirac monopoles.Comment: The final version. To appear in J. Yadernaya fizik
Geometric Approach to Lyapunov Analysis in Hamiltonian Dynamics
As is widely recognized in Lyapunov analysis, linearized Hamilton's equations
of motion have two marginal directions for which the Lyapunov exponents vanish.
Those directions are the tangent one to a Hamiltonian flow and the gradient one
of the Hamiltonian function. To separate out these two directions and to apply
Lyapunov analysis effectively in directions for which Lyapunov exponents are
not trivial, a geometric method is proposed for natural Hamiltonian systems, in
particular. In this geometric method, Hamiltonian flows of a natural
Hamiltonian system are regarded as geodesic flows on the cotangent bundle of a
Riemannian manifold with a suitable metric. Stability/instability of the
geodesic flows is then analyzed by linearized equations of motion which are
related to the Jacobi equations on the Riemannian manifold. On some geometric
setting on the cotangent bundle, it is shown that along a geodesic flow in
question, there exist Lyapunov vectors such that two of them are in the two
marginal directions and the others orthogonal to the marginal directions. It is
also pointed out that Lyapunov vectors with such properties can not be obtained
in general by the usual method which uses linearized Hamilton's equations of
motion. Furthermore, it is observed from numerical calculation for a model
system that Lyapunov exponents calculated in both methods, geometric and usual,
coincide with each other, independently of the choice of the methods.Comment: 22 pages, 14 figures, REVTeX
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
On two superintegrable nonlinear oscillators in N dimensions
We consider the classical superintegrable Hamiltonian system given by
, where U
is known to be the "intrinsic" oscillator potential on the Darboux spaces of
nonconstant curvature determined by the kinetic energy term T and parametrized
by {\lambda}. We show that H is Stackel equivalent to the free Euclidean
motion, a fact that directly provides a curved Fradkin tensor of constants of
motion for H. Furthermore, we analyze in terms of {\lambda} the three different
underlying manifolds whose geodesic motion is provided by T. As a consequence,
we find that H comprises three different nonlinear physical models that, by
constructing their radial effective potentials, are shown to be two different
nonlinear oscillators and an infinite barrier potential. The quantization of
these two oscillators and its connection with spherical confinement models is
briefly discussed.Comment: 11 pages; based on the contribution to the Manolo Gadella Fest-60
years-in-pucelandia, "Recent advances in time-asymmetric quantum mechanics,
quantization and related topics" hold in Valladolid (Spain), 14-16th july
201
Generalized Taub-NUT metrics and Killing-Yano tensors
A necessary condition that a St\"ackel-Killing tensor of valence 2 be the
contracted product of a Killing-Yano tensor of valence 2 with itself is
re-derived for a Riemannian manifold. This condition is applied to the
generalized Euclidean Taub-NUT metrics which admit a Kepler type symmetry. It
is shown that in general the St\"ackel-Killing tensors involved in the
Runge-Lenz vector cannot be expressed as a product of Killing-Yano tensors. The
only exception is the original Taub-NUT metric.Comment: 14 pages, LaTeX. Final version to appear in J.Phys.A:Math.Ge
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
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