2,408 research outputs found
Dynamics of market states and risk assessment
Based on previous developments of the concept of market states using
correlation matrices, in the present paper we address the dynamical evolution
of correlation matrices in time. This will imply minor modifications to the
market states themselves, due to increased attention to the transition matrix
between the states. We will introduce trajectories of the correlation matrices
by considering one day shifts for the epoch used to calculate the correlation
matrices and will visualize both the states and the trajectories after
dimensional scaling. This approach using dynamics improves the options of risk
assessment and opens the door to dynamical treatments of markets and shows
noise suppression in a new light.Comment: 22 pages and 27 figures. arXiv admin note: text overlap with
arXiv:2003.0705
Correlations between spectra with different symmetry: any chance to be observed?
A standard assumption in quantum chaology is the absence of correlation
between spectra pertaining to different symmetries. Doubts were raised about
this statement for several reasons, in particular, because in semiclassics
spectra of different symmetry are expressed in terms of the same set of
periodic orbits. We reexamine this question and find absence of correlation in
the universal regime. In the case of continuous symmetry the problem is reduced
to parametric correlation, and we expect correlations to be present up to a
certain time which is essentially classical but larger than the ballistic time
Invariant Manifolds and Collective Coordinates
We introduce suitable coordinate systems for interacting many-body systems
with invariant manifolds. These are Cartesian in coordinate and momentum space
and chosen such that several components are identically zero for motion on the
invariant manifold. In this sense these coordinates are collective. We make a
connection to Zickendraht's collective coordinates and present certain
configurations of few-body systems where rotations and vibrations decouple from
single-particle motion. These configurations do not depend on details of the
interaction.Comment: 15 pages, 2 EPS-figures, uses psfig.st
Nonperiodic echoes from mushroom billiard hats
Mushroom billiards have the remarkable property to show one or more clear cut
integrable islands in one or several chaotic seas, without any fractal
boundaries. The islands correspond to orbits confined to the hats of the
mushrooms, which they share with the chaotic orbits. It is thus interesting to
ask how long a chaotic orbit will remain in the hat before returning to the
stem. This question is equivalent to the inquiry about delay times for
scattering from the hat of the mushroom into an opening where the stem should
be. For fixed angular momentum we find that no more than three different delay
times are possible. This induces striking nonperiodic structures in the delay
times that may be of importance for mesoscopic devices and should be accessible
to microwave experiments.Comment: Submitted to Phys. Rev. E without the appendi
Wigner--Dyson statistics for a class of integrable models
We construct an ensemble of second--quantized Hamiltonians with two bosonic
degrees of freedom, whose members display with probability one GOE or GUE
statistics. Nevertheless, these Hamiltonians have a second integral of motion,
namely the boson number, and thus are integrable. To construct this ensemble we
use some ``reverse engineering'' starting from the fact that --bosons in a
two--level system with random interactions have an integrable classical limit
by the old Heisenberg association of boson operators to actions and angles. By
choosing an --body random interaction and degenerate levels we end up with
GOE or GUE Hamiltonians. Ergodicity of these ensembles completes the example.Comment: 3 pages, 1 figur
Charged currents, color dipoles and xF_3 at small x
We develop the light-cone color dipole description of highly asymmetric
diffractive interactions of left-handed and right-handed electroweak bosons. We
identify the origin and estimate the strength of the left-right asymmetry
effect in terms of the light-cone wave functions. We report an evaluation of
the small-x neutrino-nucleon DIS structure functions xF_3 and 2xF_1 and present
comparison with experimental data.Comment: 11 pages, 3 figures, misprints correcte
Spectral Density of the QCD Dirac Operator near Zero Virtuality
We investigate the spectral properties of a random matrix model, which in the
large limit, embodies the essentials of the QCD partition function at low
energy. The exact spectral density and its pair correlation function are
derived for an arbitrary number of flavors and zero topological charge. Their
microscopic limit provide the master formulae for sum rules for the inverse
powers of the eigenvalues of the QCD Dirac operator as recently discussed by
Leutwyler and Smilga.Comment: 9 pages + 1 figure, SUNY-NTG-93/
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