arXiv subjects

S. Drozdz

Publications and source records attributed to S. Drozdz.

48 records · Page 3Linked to original sources

arXiv1999

Dynamics of competition between collectivity and noise in the stock market

Detailed study of the financial empirical correlation matrix of the 30 companies comprised by DAX within the period of the last 11 years, using the time-window of 30 trading days, is presented. This allows to clearly identify a nontrivial time-dependence of the resulting correlations. In addition, as a rule, the draw downs are always accompanied by a sizable separation of one strong collective eigenstate of the correlation matrix which, at the same time, reduces the variance of the noise states. The opposite applies to draw ups. In this case the dynamics spreads more uniformly over the eigenstates which results in an increase of the total information entropy.

cond-mat.stat-mech↗

arXiv1999

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 $λ\approx 2$ 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.

cond-mat↗

arXiv1999

Collectivity in the Brain Sensory Response

A question of cooperative effects in auditory brain processing on various space- and time-scales is addressed. The experimental part of our study is based on Multichannel Magnetoencephalography recordings in normal human subjects. Left, right and binaural stimulations were used, in separate runs, for each subject. The resulting time-series representing left and right auditory cortex activity provide a clear evidence for two levels of neuronal cooperation. One is the local hemispheric collective response, termed M100 for its maximum at around 100ms after a stimulus onset. Its only global characteristics turn out to be time-locked to a stimulus, however, which means that the detailed neuronal evolution is largely stochastic. This, together with the $1/f$ character of the corresponding power spectrum indicates self-organized criticality as an underlying mechanism. The second level is communication between the two hemispheres with clear laterality effects: as a rule, the contralateral hemisphere leads by $\sim$10ms. Mutual information analysis points to a direct information transport as a way of this communication.

cond-mat↗

arXiv1998

Configuration Mixing Effects in Isoscalar Giant Dipole Resonance

Based on an explicit verification of the coupling matrix elements between the 1p1h and 2p2h states we propose a new method of selecting the most important 2p2h states responsible for fragmentation effects. In this way the dimensionality of the problem is reduced, such that the computation becomes feasible and the spreading of the strength is realistic, as verified by some tests of convergence. Calculations in $^{208}$Pb show that due to sizable mixing effects only about 50% of the total isoscalar giant dipole resonance (ISGDR) $3\hbarω$ strength is located in the energy region between 20 and 25 MeV. This is the energy region which currently is available in experiment. Even above 30 MeV we find about 10% of the total strength. This indicates that the current experimantal evaluations of the ISGDR centroid energy may significantly underestimate its value.

nucl-th↗

arXiv1998

Cooperative dynamics in auditory brain response

Simultaneous estimates of the activity in the left and right auditory cortex of five normal human subjects were extracted from Multichannel Magnetoencephalography recordings. Left, right and binaural stimulation were used, in separate runs, for each subject. The resulting time-series of left and right auditory cortex activity were analysed using the concept of mutual information. The analysis constitutes an objective method to address the nature of inter-hemispheric correlations in response to auditory stimulations. The results provide a clear evidence for the occurrence of such correlations mediated by a direct information transport, with clear laterality effects: as a rule, the contralateral hemisphere leads by 10-20ms, as can be seen in the average signal. The strength of the inter-hemispheric coupling, which cannot be extracted from the average data, is found to be highly variable from subject to subject, but remarkably stable for each subject.

physics.bio-ph↗

arXiv1997

Collectivity Embedded in Complex Spectra of Finite Interacting Fermi Systems: Nuclear Example

The mechanism of collectivity coexisting with chaos in a finite system of strongly interacting fermions is investigated. The complex spectra are represented in the basis of two-particle two-hole states describing the nuclear double-charge exchange modes in $^{48}$Ca. An example of $J^π=0^-$ excitations shows that the residual interaction, which generically implies chaotic behavior, under certain specific and well identified conditions may create strong transitions, even much stronger than those corresponding to a pure mean-field picture. Such an effect results from correlations among the off-diagonal matrix elements, is connected with locally reduced density of states and a local minimum in the information entropy.

chao-dyn↗

arXiv1997

Scaling Properties of Nuclear Giant Resonance Transition Probabilities

Multifractal scaling analysis of nuclear giant resonance transition probability distributions is performed within the approximation which takes into account the one-particle-one-hole (1p-1h) and 2p-2h states. A new measure to determine the fractal dimensions of the spectra is introduced. It is found that chaotic dynamics governing the decay leads to non-trivial multifractal scaling properties. Such a kind of scaling is absent in the case of regular dynamics. The degree of collectivity is another element which worsens the scaling.

nucl-th↗

arXiv1997

Collectivity Embedded in Complex Spectra: Example of Nuclear Double-Charge Exchange Modes

The mechanism of collectivity coexisting with chaos is investigated on the quantum level. The complex spectra are represented in the basis of two-particle two-hole states describing the nuclear double-charge exchange modes in $^{48}$Ca. An example of $J^π=0^-$ excitations shows that the residual interaction, which generically implies chaotic behavior, under certain specific and well identified conditions may create transitions stronger than those corresponding to the pure mean-field picture. Therefore, for this type of excitations such an effect is not generic and in most cases the strength of transitions is likely to take much lower values, even close to the Porter-Thomas distributed.

nucl-th↗

arXiv1996

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.

chao-dyn↗

arXiv1994

Phase-Space Exploration in Nuclear Giant Resonance Decay

The rate of phase-space exploration in the decay of isovector and isoscalar giant quadrupole resonances in $^{40}$Ca is analyzed. The study is based on the time dependence of the survival probability and of the spectrum of generalized entropies evaluated in the space of 1p-1h and 2p-2h states. If the 2p-2h background shows the characteristics typical for chaotic systems, the isovector excitation evolves almost statistically while the isoscalar excitation remains largely localized, even though it penetrates the whole available phase space.

nucl-th↗

arXiv1993

Chaos Driven Decay of Nuclear Giant Resonances: Route to Quantum Self-Organization

The influence of background states with increasing level of complexity on the strength distribution of the isoscalar and isovector giant quadrupole resonance in $^{40}$Ca is studied. It is found that the background characteristics, typical for chaotic systems, strongly affects the fluctuation properties of the strength distribution. In particular, the small components of the wave function obey a scaling law analogous to self-organized systems at the critical state. This appears to be consistent with the Porter-Thomas distribution of the transition strength.

nucl-th↗

arXiv1993

Modeling Complex Nuclear Spectra - Regularity versus Chaos

A statistical analysis of the spectrum of two particle - two hole doorway states in a finite nucleus is performed. On the unperturbed mean-field level sizable attractive correlations are present in such a spectrum. Including particle-hole rescattering effects via the residual interaction introduces repulsive dynamical correlations which generate the fluctuation properties characteristic of the Gaussian Orthogonal Ensemble. This signals that the underlying dynamics becomes chaotic. This feature turns out to be independent of the detailed form of the residual interaction and hence reflects the generic nature of the fluctuations studied.

nucl-th↗