Fractal fractal dimensions of deterministic transport coefficients

If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze the structure of the associated irregular diffusion coefficient and current by numerically computing dimensions from box-counting and from the autocorrelation function of these graphs. We find that both dimensions are fractal for large parameter intervals and that both quantities are themselves fractal functions if computed locally on a uniform grid of small but finite subintervals. We furthermore show that there is a simple functional relationship between the structure of fractal fractal dimensions and the difference quotient defined on these subintervals.Comment: 16 pages (revtex) with 6 figures (postscript

Fractal dimension of transport coefficients in a deterministic dynamical system

In many low-dimensional dynamical systems transport coefficients are very irregular, perhaps even fractal functions of control parameters. To analyse this phenomenon we study a dynamical system defined by a piece-wise linear map and investigate the dependence of transport coefficients on the slope of the map. We present analytical arguments, supported by numerical calculations, showing that both the Minkowski-Bouligand and Hausdorff fractal dimension of the graphs of these functions is 1 with a logarithmic correction, and find that the exponent $\gamma$ controlling this correction is bounded from above by 1 or 2, depending on some detailed properties of the system. Using numerical techniques we show local self-similarity of the graphs. The local self-similarity scaling transformations turn out to depend (irregularly) on the values of the system control parameters.Comment: 17 pages, 6 figures; ver.2: 18 pages, 7 figures (added section 5.2, corrected typos, etc.

Understanding deterministic diffusion by correlated random walks

Low-dimensional periodic arrays of scatterers with a moving point particle are ideal models for studying deterministic diffusion. For such systems the diffusion coefficient is typically an irregular function under variation of a control parameter. Here we propose a systematic scheme of how to approximate deterministic diffusion coefficients of this kind in terms of correlated random walks. We apply this approach to two simple examples which are a one-dimensional map on the line and the periodic Lorentz gas. Starting from suitable Green-Kubo formulas we evaluate hierarchies of approximations for their parameter-dependent diffusion coefficients. These approximations converge exactly yielding a straightforward interpretation of the structure of these irregular diffusion coeficients in terms of dynamical correlations.Comment: 13 pages (revtex) with 5 figures (postscript

Deterministic diffusion in flower shape billiards

We propose a flower shape billiard in order to study the irregular parameter dependence of chaotic normal diffusion. Our model is an open system consisting of periodically distributed obstacles of flower shape, and it is strongly chaotic for almost all parameter values. We compute the parameter dependent diffusion coefficient of this model from computer simulations and analyze its functional form by different schemes all generalizing the simple random walk approximation of Machta and Zwanzig. The improved methods we use are based either on heuristic higher-order corrections to the simple random walk model, on lattice gas simulation methods, or they start from a suitable Green-Kubo formula for diffusion. We show that dynamical correlations, or memory effects, are of crucial importance to reproduce the precise parameter dependence of the diffusion coefficent.Comment: 8 pages (revtex) with 9 figures (encapsulated postscript

Investigations on nucleophilic layers made with a novel plasma jet technique

In this work a novel plasma jet technique is used for the deposition of nucleophilic films based on (3-aminopropyl)trimethoxysilane at atmospheric pressure. Film deposition was varied with regard to duty cycles and working distance. Spectral ellipsometry and chemical derivatization with 4-(trifluoromethyl)benzaldehyde using ATR- FTIR spectroscopy measurements were used to characterize the films. It was found that the layer thickness and the film composition are mainly influenced by the duty cycle

Neutron-induced background in the CONUS experiment

CONUS is a novel experiment aiming at detecting elastic neutrino nucleus scattering in the fully coherent regime using high-purity Germanium (Ge) detectors and a reactor as antineutrino ($\bar\nu$) source. The detector setup is installed at the commercial nuclear power plant in Brokdorf, Germany, at a very small distance to the reactor core in order to guarantee a high flux of more than 10$^{13}\bar\nu$/(s$\cdot$cm$^2$). For the experiment, a good understanding of neutron-induced background events is required, as the neutron recoil signals can mimic the predicted neutrino interactions. Especially neutron-induced events correlated with the thermal power generation are troublesome for CONUS. On-site measurements revealed the presence of a thermal power correlated, highly thermalized neutron field with a fluence rate of (745$\pm$30)cm$^{-2}$d$^{-1}$. These neutrons that are produced by nuclear fission inside the reactor core, are reduced by a factor of $\sim$10$^{20}$ on their way to the CONUS shield. With a high-purity Ge detector without shield the $\gamma$-ray background was examined including highly thermal power correlated $^{16}$N decay products as well as $\gamma$-lines from neutron capture. Using the measured neutron spectrum as input, it was shown, with the help of Monte Carlo simulations, that the thermal power correlated field is successfully mitigated by the installed CONUS shield. The reactor-induced background contribution in the region of interest is exceeded by the expected signal by at least one order of magnitude assuming a realistic ionization quenching factor of 0.2.Comment: 28 pages, 28 figure

Is subdiffusional transport slower than normal?

We consider anomalous non-Markovian transport of Brownian particles in viscoelastic fluid-like media with very large but finite macroscopic viscosity under the influence of a constant force field F. The viscoelastic properties of the medium are characterized by a power-law viscoelastic memory kernel which ultra slow decays in time on the time scale \tau of strong viscoelastic correlations. The subdiffusive transport regime emerges transiently for t<\tau. However, the transport becomes asymptotically normal for t>>\tau. It is shown that even though transiently the mean displacement and the variance both scale sublinearly, i.e. anomalously slow, in time, ~ F t^\alpha, ~ t^\alpha, 0<\alpha<1, the mean displacement at each instant of time is nevertheless always larger than one obtained for normal transport in a purely viscous medium with the same macroscopic viscosity obtained in the Markovian approximation. This can have profound implications for the subdiffusive transport in biological cells as the notion of "ultra-slowness" can be misleading in the context of anomalous diffusion-limited transport and reaction processes occurring on nano- and mesoscales

Twisting of light around rotating black holes

Kerr black holes are among the most intriguing predictions of Einstein's general relativity theory. These rotating massive astrophysical objects drag and intermix their surrounding space and time, deflecting and phase-modifying light emitted nearby them. We have found that this leads to a new relativistic effect that imposes orbital angular momentum onto such light. Numerical experiments, based on the integration of the null geodesic equations of light from orbiting point-like sources in the Kerr black hole equatorial plane to an asymptotic observer, indeed identify the phase change and wavefront warping and predict the associated light-beam orbital angular momentum spectra. Setting up the best existing telescopes properly, it should be possible to detect and measure this twisted light, thus allowing a direct observational demonstration of the existence of rotating black holes. Since non-rotating objects are more an exception than a rule in the Universe, our findings are of fundamental importance.Comment: Article: 18 pages (11 pages in form of an Appendix). Total number of figures:

Diffusion in normal and critical transient chaos

In this paper we investigate deterministic diffusion in systems which are spatially extended in certain directions but are restricted in size and open in other directions, consequently particles can escape. We introduce besides the diffusion coefficient D on the chaotic repeller a coefficient ${\hat D}$ which measures the broadening of the distribution of trajectories during the transient chaotic motion. Both coefficients are explicitly computed for one-dimensional models, and they are found to be different in most cases. We show furthermore that a jump develops in both of the coefficients for most of the initial distributions when we approach the critical borderline where the escape rate equals the Liapunov exponent of a periodic orbit.Comment: 4 pages Revtex file in twocolumn format with 2 included postscript figure

Escape Behavior of Quantum Two-Particle Systems with Coulomb Interactions

Quantum escapes of two particles with Coulomb interactions from a confined one-dimensional region to a semi-infinite lead are discussed by the probability of particles remaining in the confined region, i.e. the survival probability, in comparison with one or two free particles. For free-particle systems the survival probability decays asymptotically in power as a function of time. On the other hand, for two-particle systems with Coulomb interactions it shows an exponential decay in time. A difference of escape behaviors between Bosons and Fermions is considered as quantum effects of identical two particles such as the Pauli exclusion principle. The exponential decay in the survival probability of interacting two particles is also discussed in a viewpoint of quantum chaos based on a distribution of energy level spacings.Comment: 10 pages, 7 figure