Chaos induced by Pauli blocking

Dynamics of classical scattering in the system of fermions is studied. The model is based on the coherent state representation and the equations of motion for fermions are derived from the time-dependent variational principle. It is found that the antisymmetrization due to the Pauli exclusion principle, may lead to hyperbolic chaotic scattering even in the absence of interaction between particles. At low bombarding energies, the same effect leads to the screening of the hard, short-ranged component in the two particle interaction and thus regularizes the dynamics.Comment: 10 pages, LaTeX

Spectral Decorrelation of Nuclear Levels in the Presence of Continuum Decay

The fluctuation properties of nuclear giant resonance spectra are studied in the presence of continuum decay. The subspace of quasi-bound states is specified by one-particle one-hole and two-particle two-hole excitations and the continuum coupling is generated by a scattering ensemble. It is found that, with increasing number of open channels, the real parts of the complex eigenvalues quickly decorrelate. This appears to be related to the transition from power-law to exponential time behavior of the survival probability of an initially non-stationary state.Comment: 10 Pages, REVTEX, 4 PostScript figure

Molecular dynamics approach: from chaotic to statistical properties of compound nuclei

Statistical aspects of the dynamics of chaotic scattering in the classical model of $\alpha$-cluster nuclei are studied. It is found that the dynamics governed by hyperbolic instabilities which results in an exponential decay of the survival probability evolves to a limiting energy distribution whose density develops the Boltzmann form. The angular distribution of the corresponding decay products shows symmetry with respect to $\pi/2$ angle. Time estimated for the compound nucleus formation ranges within the order of $10^{-21}$s.Comment: 11 pages, LaTeX, non

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 $J^{\pi}=0^-$ 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.Comment: 16 pages, LaTeX2e, REVTeX, 8 PostScript figures, to appear in Physical Review

Asymmetric correlation matrices: an analysis of financial data

We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson correlation matrices to the realm of complex eigenvalues. We employ some recent random matrix theory results on the average eigenvalue density of this type of matrices to distinguish between noise and non trivial correlation structures, and we focus on financial data as a case study. Namely, we employ daily prices of stocks belonging to the American and British stock exchanges, and look for the emergence of correlations between two such markets in the eigenvalue spectrum of their non symmetric correlation matrix. We find several non trivial results, also when considering time-lagged correlations over short lags, and we corroborate our findings by additionally studying the asymmetric correlation matrix of the principal components of our datasets.Comment: Revised version; 11 pages, 13 figure

Multiscale fluctuations in nuclear response

The nuclear collective response is investigated in the framework of a doorway picture in which the spreading width of the collective motion is described as a coupling to more and more complex configurations. It is shown that this coupling induces fluctuations of the observed strength. In the case of a hierarchy of overlapping decay channels, we observe Ericson fluctuations at different scales. Methods for extracting these scales and the related lifetimes are discussed. Finally, we show that the coupling of different states at one level of complexity to some common decay channels at the next level, may produce interference-like patterns in the nuclear response. This quantum effect leads to a new type of fluctuations with a typical width related to the level spacing.Comment: 34 Latex pages including 6 figures (submitted to Phys. Rev. C

Whispering gallery modes in open quantum billiards

The poles of the S-matrix and the wave functions of open 2D quantum billiards with convex boundary of different shape are calculated by the method of complex scaling. Two leads are attached to the cavities. The conductance of the cavities is calculated at energies with one, two and three open channels in each lead. Bands of overlapping resonance states appear which are localized along the convex boundary of the cavities and contribute coherently to the conductance. These bands correspond to the whispering gallery modes appearing in the classical calculations.Comment: 9 pages, 3 figures in jpg and gif forma

Comprehensive Analysis of Market Conditions in the Foreign Exchange Market: Fluctuation Scaling and Variance-Covariance Matrix

We investigate quotation and transaction activities in the foreign exchange market for every week during the period of June 2007 to December 2010. A scaling relationship between the mean values of number of quotations (or number of transactions) for various currency pairs and the corresponding standard deviations holds for a majority of the weeks. However, the scaling breaks in some time intervals, which is related to the emergence of market shocks. There is a monotonous relationship between values of scaling indices and global averages of currency pair cross-correlations when both quantities are observed for various window lengths $\Delta t$.Comment: 13 pages, 10 figure

Regular spectra in the vibron model with random interactions

The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the vibron model. A mean-field analysis links different regions of the parameter space with definite geometric shapes. The results that are, to a large extent, obtained in closed analytic form, provide a clear and transparent interpretation of the high degree of order that has been observed in numerical studies.Comment: 19 pages, 8 figures, 2 tables. Physical Review C, in pres