12,663 research outputs found
When are projections also embeddings?
We study an autonomous four-dimensional dynamical system used to model certain geophysical processes.This system generates a chaotic attractor that is strongly contracting, with four Lyapunov exponents that satisfy , so the Lyapunov dimension is in the range of coupling parameter values studied. As a result, it should be possible to find three-dimensional spaces in which the attractors can be embedded so that topological analyses can be carried out to determine which stretching and squeezing mechanisms generate chaotic behavior. We study mappings into to determine which can be used as embeddings to reconstruct the dynamics. We find dramatically different behavior in the two simplest mappings: projections from to . In one case the one-parameter family of attractors studied remains topologically unchanged for all coupling parameter values. In the other case, during an intermediate range of parameter values the projection undergoes self-intersections, while the embedded attractors at the two ends of this range are topologically mirror images of each other
A Comparison of Tests for Embeddings
It is possible to compare results for the classical tests for embeddings of chaotic data with the results of a recently proposed test. The classical tests, which depend on real numbers (fractal dimensions, Lyapunov exponents) averaged over an attractor, are compared with a topological test that depends on integers. The comparison can only be done for mappings into three dimensions. We find that the classical tests fail to predict when a mapping is an embedding and when it is not. We point out the reasons for this failure, which are not restricted to three dimensions
Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schroedinger equation
We characterize the full family of soliton solutions sitting over a
background plane wave and ruled by the cubic-quintic nonlinear Schroedinger
equation in the regime where a quintic focusing term represents a saturation of
the cubic defocusing nonlinearity. We discuss existence and properties of
solitons in terms of catastrophe theory and fully characterize bistability and
instabilities of the dark-antidark pairs, revealing new mechanisms of decay of
antidark solitons.Comment: 8 pages, 10 figures, accepted in PR
Generalized coherent states are unique Bell states of quantum systems with Lie group symmetries
We consider quantum systems, whose dynamical symmetry groups are semisimple
Lie groups, which can be split or decay into two subsystems of the same
symmetry. We prove that the only states of such a system that factorize upon
splitting are the generalized coherent states. Since Bell's inequality is never
violated by the direct product state, when the system prepared in the
generalized coherent state is split, no quantum correlations are created.
Therefore, the generalized coherent states are the unique Bell states, i.e.,
the pure quantum states preserving the fundamental classical property of
satisfying Bell's inequality upon splitting.Comment: 4 pages, REVTeX, amssymb style. More information on
http://www.technion.ac.il/~brif/science.htm
Self-Dual Yang-Mills and Vector-Spinor Fields, Nilpotent Fermionic Symmetry, and Supersymmetric Integrable Systems
We present a system of a self-dual Yang-Mills field and a self-dual
vector-spinor field with nilpotent fermionic symmetry (but not supersymmetry)
in 2+2 dimensions, that generates supersymmetric integrable systems in lower
dimensions. Our field content is (A_\mu{}^I, \psi_\mu{}^I, \chi^{I J}), where I
and J are the adjoint indices of arbitrary gauge group. The \chi^{I J} is a
Stueckelberg field for consistency. The system has local nilpotent fermionic
symmetry with the algebra \{N_\alpha{}^I, N_\beta{}^J \} = 0. This system
generates supersymmetric Kadomtsev-Petviashvili equations in D=2+1, and
supersymmetric Korteweg-de Vries equations in D=1+1 after appropriate
dimensional reductions. We also show that a similar self-dual system in seven
dimensions generates self-dual system in four dimensions. Based on our results
we conjecture that lower-dimensional supersymmetric integral models can be
generated by non-supersymmetric self-dual systems in higher dimensions only
with nilpotent fermionic symmetries.Comment: 15 pages, no figure
On N=8 attractors
We derive and solve the black hole attractor conditions of N=8 supergravity
by finding the critical points of the corresponding black hole potential. This
is achieved by a simple generalization of the symplectic structure of the
special geometry to all extended supergravities with .
There are two solutions for regular black holes, one for 1/8 BPS ones and one
for the non-BPS. We discuss the solutions of the moduli at the horizon for BPS
attractors using N=2 language. An interpretation of some of these results in
N=2 STU black hole context helps to clarify the general features of the black
hole attractors.Comment: 15 page
Topological phase for entangled two-qubit states and the representation of the SO(3)group
We discuss the representation of the group by two-qubit maximally
entangled states (MES). We analyze the correspondence between and the
set of two-qubit MES which are experimentally realizable. As a result, we offer
a new interpretation of some recently proposed experiments based on MES.
Employing the tools of quantum optics we treat in terms of two-qubit MES some
classical experiments in neutron interferometry, which showed the -phase
accrued by a spin- particle precessing in a magnetic field. By so doing,
we can analyze the extent to which the recently proposed experiments - and
future ones of the same sort - would involve essentially new physical aspects
as compared with those performed in the past. We argue that the proposed
experiments do extend the possibilities for displaying the double connectedness
of , although for that to be the case it results necessary to map
elements of onto physical operations acting on two-level systems.Comment: 25 pages, 9 figure
Scaling Laws for Incipient Cavitation Noise
The noise produced by the motion or a body through a liquid differs from that produced by the motion of a body through a gas because of the possibility or cavitation in the liquid case. An adequate theory or cavitation and cavitation noise is not yet available, but the application
or dimensional analysis together with the theoretical information so far obtained can yield scaling laws for this flow situation.
In section II, a brief dissussion will be given or the scaling laws
for hydrodynamic noise in some cases of non-cavitating flow; this discussion is included tor oompleteness. In section III, a summary or the
present information on the scaling law. for incipient cavitation noise will be presented
Calculation of the unitary part of the Bures measure for N-level quantum systems
We use the canonical coset parameterization and provide a formula with the
unitary part of the Bures measure for non-degenerate systems in terms of the
product of even Euclidean balls. This formula is shown to be consistent with
the sampling of random states through the generation of random unitary
matrices
Kinematics of Nearby Subdwarf Stars
We present an analysis of the space motions of 742 subdwarf stars based on
the sample of Carney et al. (1994, CLLA). Hipparcos parallaxes, TYC2+HIP proper
motions and Tycho2 proper motions were combined with radial velocities and
metallicities from CLLA. The kinematical behavior is discussed in particular in
relation to their metallicities. The majority of these sample stars have metal
abundances of [Fe/H] >-1 and represent the thick disk population. The halo
component, with [Fe/H] <-1.6, is characterized by a low mean rotation velocity
and a radially elongated velocity ellipsoid. In the intermediate metallicity
range (-1.6 < [Fe/H] <-1), we find a significant number of subdwarfs with
disklike kinematics. We interpret this population of stars as a metal-weak
thick disk population.Comment: 6 pages, 7 figures, accepted by Astronomy & Astrophysic
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