8,615 research outputs found
Chaos in the BMN matrix model
We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN)
matrix model. For this purpose, it is convenient to focus upon a reduced system
composed of two-coupled anharmonic oscillators by supposing an ansatz. We
examine three ans\"atze: 1) two pulsating fuzzy spheres, 2) a single
Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two
cases, we show the existence of chaos by computing Poincar\'e sections and a
Lyapunov spectrum. The third case leads to an integrable system. As a result,
the BMN matrix model is not integrable in the sense of Liouville, though there
may be some integrable subsectors.Comment: 23 pages, 15 figures, v2: further clarifications and references adde
Almost periodic solutions of retarded SICNNs with functional response on piecewise constant argument
We consider a new model for shunting inhibitory cellular neural networks,
retarded functional differential equations with piecewise constant argument.
The existence and exponential stability of almost periodic solutions are
investigated. An illustrative example is provided.Comment: 24 pages, 1 figur
Almost automorphic delayed differential equations and Lasota-Wazewska model
Existence of almost automorphic solutions for abstract delayed differential
equations is established. Using ergodicity, exponential dichotomy and Bi-almost
automorphicity on the homogeneous part, sufficient conditions for the existence
and uniqueness of almost automorphic solutions are given.Comment: 16 page
Quantum mechanics on non commutative spaces and squeezed states: a functional approach
We review here the quantum mechanics of some noncommutative theories in which
no state saturates simultaneously all the non trivial Heisenberg uncertainty
relations. We show how the difference of structure between the Poisson brackets
and the commutators in these theories generically leads to a harmonic
oscillator whose positions and momenta mean values are not strictly equal to
the ones predicted by classical mechanics.
This raises the question of the nature of quasi classical states in these
models. We propose an extension based on a variational principle. The action
considered is the sum of the absolute values of the expressions associated to
the non trivial Heisenberg uncertainty relations. We first verify that our
proposal works in the usual theory i.e we recover the known Gaussian functions.
Besides them, we find other states which can be expressed as products of
Gaussians with specific hyper geometrics.
We illustrate our construction in two models defined on a four dimensional
phase space: a model endowed with a minimal length uncertainty and the non
commutative plane. Our proposal leads to second order partial differential
equations. We find analytical solutions in specific cases. We briefly discuss
how our proposal may be applied to the fuzzy sphere and analyze its
shortcomings.Comment: 15 pages revtex. The title has been modified,the paper shortened and
misprints have been corrected. Version to appear in JHE
Magnetic operations: a little fuzzy physics?
We examine the behaviour of charged particles in homogeneous, constant and/or
oscillating magnetic fields in the non-relativistic approximation. A special
role of the geometric center of the particle trajectory is elucidated. In
quantum case it becomes a 'fuzzy point' with non-commuting coordinates, an
element of non-commutative geometry which enters into the traditional control
problems. We show that its application extends beyond the usually considered
time independent magnetic fields of the quantum Hall effect. Some simple cases
of magnetic control by oscillating fields lead to the stability maps differing
from the traditional Strutt diagram.Comment: 28 pages, 8 figure
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