Chaos or Noise - Difficulties of a Distinction

In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high embedding dimension. These restrictions limit our ability to distinguish between signals generated by different systems, such as regular, chaotic or stochastic ones, when analyzed from a time series point of view. We propose to classify the signal behavior, without referring to any specific model, as stochastic or deterministic on a certain scale of the resolution $\epsilon$, according to the dependence of the $(\epsilon,\tau)$-entropy, $h(\epsilon, \tau)$, and of the finite size Lyapunov exponent, $\lambda(\epsilon)$, on $\epsilon$.Comment: 24 pages RevTeX, 9 eps figures included, two references added, minor corrections, one section has been split in two (submitted to PRE

Local estimates for entropy densities in coupled map lattices

We present a method to derive an upper bound for the entropy density of coupled map lattices with local interactions from local observations. To do this, we use an embedding technique being a combination of time delay and spatial embedding. This embedding allows us to identify the local character of the equations of motion. Based on this method we present an approximate estimate of the entropy density by the correlation integral.Comment: 4 pages, 5 figures include

Room temperature high frequency transport of Dirac fermions in epitaxially grown Sb_2Te_3 based topological insulators

We report on the observation of photogalvanic effects in epitaxially grown Sb_2Te_3 three-dimensional (3D) topological insulators (TI). We show that asymmetric scattering of Dirac electrons driven back and forth by the terahertz electric field results in a dc electric current. Due to the "symmetry filtration" the dc current is generated in the surface electrons only and provides an opto-electronic access to probe the electric transport in TI, surface domains orientation and details of electron scattering even in 3D TI at room temperature where conventional surface electron transport is usually hindered by the high carrier density in the bulk

Detecting Determinism in High Dimensional Chaotic Systems

A method based upon the statistical evaluation of the differentiability of the measure along the trajectory is used to identify in high dimensional systems. The results show that the method is suitable for discriminating stochastic from deterministic systems even if the dimension of the latter is as high as 13. The method is shown to succeed in identifying determinism in electro-encephalogram signals simulated by means of a high dimensional system.Comment: 8 pages (RevTeX 3 style), 5 EPS figures, submitted to Phys. Rev. E (25 apr 2001

Suppression of quantum oscillations and the dependence on site energies in electronic excitation transfer in the Fenna-Matthews-Olson trimer

Energy transfer in the photosynthetic complex of the Green Sulfur Bacteria known as the Fenna-Matthews-Olson (FMO) complex is studied theoretically taking all three subunits (monomers) of the FMO trimer and the recently found eighth bacteriochlorophyll (BChl) molecule into account. We find that in all considered cases there is very little transfer between the monomers. Since it is believed that the eighth BChl is located near the main light harvesting antenna we look at the differences in transfer between the situation when BChl 8 is initially excited and the usually considered case when BChl 1 or 6 is initially excited. We find strong differences in the transfer dynamics, both qualitatively and quantitatively. When the excited state dynamics is initialized at site eight of the FMO complex, we see a slow exponential-like decay of the excitation. This is in contrast to the oscillations and a relatively fast transfer that occurs when only seven sites or initialization at sites 1 and 6 is considered. Additionally we show that differences in the values of the electronic transition energies found in the literature lead to a large difference in the transfer dynamics

Structure Factor and Electronic Structure of Compressed Liquid Rubidium

We have applied the quantal hypernetted-chain equations in combination with the Rosenfeld bridge-functional to calculate the atomic and the electronic structure of compressed liquid-rubidium under high pressure (0.2, 2.5, 3.9, and 6.1 GPa); the calculated structure factors are in good agreement with experimental results measured by Tsuji et al. along the melting curve. We found that the Rb-pseudoatom remains under these high pressures almost unchanged with respect to the pseudoatom at room pressure; thus, the effective ion-ion interaction is practically the same for all pressure-values. We observe that all structure factors calculated for this pressure-variation coincide almost into a single curve if wavenumbers are scaled in units of the Wigner-Seitz radius $a$ although no corresponding scaling feature is observed in the effective ion-ion interaction.This scaling property of the structure factors signifies that the compression in liquid-rubidium is uniform with increasing pressure; in absolute Q-values this means that the first peak-position ($Q_1$) of the structure factor increases proportionally to $V^{-1/3}$ ($V$ being the specific volume per ion), as was experimentally observed by Tsuji et al.Comment: 18 pages, 11 figure

Algorithm for J-Integral Measurements by Digital Image Correlation

The work is devoted to the testing of the algorithm for calculating J-integral based on the construction of vector fields by digital image correlation (DIC) method. A comparative analysis of J-integral values calculated using DIC and instrumental data obtained in accordance with ASTM E 1820 "Standard Test Method for Measurement of Fracture Toughness" has made. It is shown that this approach can be used for cases when the standard technique for measuring the J-integral cannot be applied, or the standard technique does not allow achieving the required accuracy for the integral determination in local areas of the loaded material