445 research outputs found
Imprints of log-periodic self-similarity in the stock market
Detailed analysis of the log-periodic structures as precursors of the
financial crashes is presented. The study is mainly based on the German Stock
Index (DAX) variation over the 1998 period which includes both, a spectacular
boom and a large decline, in magnitude only comparable to the so-called Black
Monday of October 1987. The present example provides further arguments in
favour of a discrete scale-invariance governing the dynamics of the stock
market. A related clear log-periodic structure prior to the crash and
consistent with its onset extends over the period of a few months. Furthermore,
on smaller time-scales the data seems to indicate the appearance of analogous
log-periodic oscillations as precursors of the smaller, intermediate decreases.
Even the frequencies of such oscillations are similar on various levels of
resolution. The related value of preferred scaling ratios
is amazingly consistent with those found for a wide variety of other complex
systems. Similar analysis of the major American indices between September 1998
and February 1999 also provides some evidence supporting this concept but, at
the same time, illustrates a possible splitting of the dynamics that a large
market may experience.Comment: 13 pages, LaTeX-REVTeX, 4 PS figures. Significantly extended version
to appear in The European Physical Journal
Decay of Nuclear Giant Resonances: Quantum Self-similar Fragmentation
Scaling analysis of nuclear giant resonance transition probabilities with
increasing level of complexity in the background states is performed. It is
found that the background characteristics, typical for chaotic systems lead to
nontrivial multifractal scaling properties.Comment: 4 pages, LaTeX format, pc96.sty + 2 eps figures, accepted as: talk at
the 8th Joint EPS-APS International Conference on Physics Computing (PC'96,
17-21. Sept. 1996), to appear in the Proceeding
Statistical aspects of nuclear coupling to continuum
Various global characteristics of the coupling between the bound and scattering states are explicitly studied based on realistic Shell Model Embedded in the Continuum. In particular, such characteristics are related to those of the scattering ensemble. It is found that in the region of higher density of states the coupling to continuum is largely consistent with the statistical model. However, assumption of channel equivalence in the statistical model is, in general, violated
Pathological Behavior in the Spectral Statistics of the Asymmetric Rotor Model
The aim of this work is to study the spectral statistics of the asymmetric
rotor model (triaxial rigid rotator). The asymmetric top is classically
integrable and, according to the Berry-Tabor theory, its spectral statistics
should be Poissonian. Surprisingly, our numerical results show that the nearest
neighbor spacing distribution and the spectral rigidity do
not follow Poisson statistics. In particular, shows a sharp peak at
while for small values of follows the Poissonian
predictions and asymptotically it shows large fluctuations around its mean
value. Finally, we analyze the information entropy, which shows a dissolution
of quantum numbers by breaking the axial symmetry of the rigid rotator.Comment: 11 pages, 7 figures, to be published in Phys. Rev.
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
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