Decohering localized waves

In the absence of confinement localization of waves takes place due to randomness or nonlinearity and relies on their phase coherence. We quantitatively probe the sensitivity of localized wave packets to random phase fluctuations and confirm the necessity of phase coherence for localization. Decoherence resulting from a dynamical random environment leads to diffusive spreading and destroys linear and nonlinear localization. We find that maximal spreading is achieved for optimal phase fluctuation characteristics which is a consequence of the competition between diffusion due to decoherence and ballistic transport within the mean free path distance.Comment: Updated affiliatio

New approaches for automated data processing of annually laminated sediments

International audienceLaminated sediments, like evaporites and biogenic lake sediments, provide high-resolution paleo-climate records. Yet detection and counting of laminae causes still problems because sedimentary structures are often disturbed. In the past laminated rocks often were analysed manually - a tedious and subjective work. The present study describes four automated approaches for lamina detection based on 1d grey-scale vectors. Best results are obtained with a newly developed algorithm, called Adaptive Template Method (ATM) in combination with the Hilbert transform. ATM improves the signal to noise ratio of the grey-value signal. Its basic idea is to extract first a characteristic waveform, the template, which describes the typical grey-value variation transverse to the laminae. This is a kind of "template learning" process, which in practice is done by an appropriate averaging method. This template is in a second step used for processing the whole sample. One calculates the overlap of the template with the actual signal, the grey-value variation along the core, as function of position in core direction. This method generates a new signal with maxima at positions, where the template optimally matches the original signal. The new time-series is called AT-transform. It is smoother than the initial data sequence. High frequency noise and local trend effects are suppressed. Afterwards, the AT-transform can be analysed with the Hilbert transformation for extracting phase information. The data processing methods are tested both on artificial data sequences and on a seasonally laminated sedimentary record of the Oligocene Baruth Maar (Germany). Although ATM is no panacea for highly disturbed signals, our comparison with other approaches shows that it provides the best results. The combination of ATM and the Hilbert transform allows to detect clearly long-term oscillations in the sedimentation patterns and thus cycles in climatic variations

Understanding highly excited states via parametric variations

Highly excited vibrational states of an isolated molecule encode the vibrational energy flow pathways in the molecule. Recent studies have had spectacular success in understanding the nature of the excited states mainly due to the extensive studies of the classical phase space structures and their bifurcations. Such detailed classical-quantum correspondence studies are presently limited to two or quasi two dimensional systems. One of the main reasons for such a constraint has to do with the problem of visualization of relevant objects like surface of sections and Wigner or Husimi distributions associated with an eigenstate. This neccesiates various alternative techniques which are more algebraic than geometric in nature. In this work we introduce one such method based on parametric variation of the eigenvalues of a Hamiltonian. It is shown that the level velocities are correlated with the phase space nature of the corresponding eigenstates. A semiclassical expression for the level velocities of a single resonance Hamiltonian is derived which provides theoretical support for the correlation. We use the level velocities to dynamically assign the highly excited states of a model spectroscopic Hamiltonian in the mixed phase space regime. The effect of bifurcations on the level velocities is briefly discussed using a recently proposed spectroscopic Hamiltonian for the HCP molecule.Comment: 12 pages, 9 figures, submitted to J. Chem. Phy

Analyzing intramolecular vibrational energy redistribution via the overlap intensity-level velocity correlator

Numerous experimental and theoretical studies have established that intramolecular vibrational energy redistribution (IVR) in isolated molecules has a heirarchical tier structure. The tier structure implies strong correlations between the energy level motions of a quantum system and its intensity-weighted spectrum. A measure, which explicitly accounts for this correaltion, was first introduced by one of us as a sensitive probe of phase space localization. It correlates eigenlevel velocities with the overlap intensities between the eigenstates and some localized state of interest. A semiclassical theory for the correlation is developed for systems that are classically integrable and complements earlier work focusing exclusively on the chaotic case. Application to a model two dimensional effective spectroscopic Hamiltonian shows that the correlation measure can provide information about the terms in the molecular Hamiltonian which play an important role in an energy range of interest and the character of the dynamics. Moreover, the correlation function is capable of highlighting relevant phase space structures including the local resonance features associated with a specific bright state. In addition to being ideally suited for multidimensional systems with a large density of states, the measure can also be used to gain insights into the phase space transport and localization. It is argued that the overlap intensity-level velocity correlation function provides a novel way of studying vibrational energy redistribution in isolated molecules. The correlation function is ideally suited to analyzing the parametric spectra of molecules in external fields.Comment: 16 pages, 13 figures (low resolution

Effect of time-correlation of input patterns on the convergence of on-line learning

We studied the effects of time correlation of subsequent patterns on the convergence of on-line learning by a feedforward neural network with backpropagation algorithm. By using chaotic time series as sequences of correlated patterns, we found that the unexpected scaling of converging time with learning parameter emerges when time-correlated patterns accelerate learning process.Comment: 8 pages(Revtex), 5 figure

The randomly driven Ising ferromagnet, Part I: General formalism and mean field theory

We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast switching, random external field. After introducing a general formalism for describing such systems, we consider here the mean-field theory. A novel type of first order phase transition related to spontaneous symmetry breaking and dynamic freezing is found. The non-equilibrium stationary state has a complex structure, which changes as a function of parameters from a singular-continuous distribution with Euclidean or fractal support to an absolutely continuous one.Comment: 12 pages REVTeX/LaTeX format, 12 eps/ps figures. Submitted to Journal of Physics

Discrete model for laser driven etching and microstructuring of metallic surfaces

We present a unidimensional discrete solid-on-solid model evolving in time using a kinetic Monte Carlo method to simulate micro-structuring of kerfs on metallic surfaces by means of laser-induced jet-chemical etching. The precise control of the passivation layer achieved by this technique is responsible for the high resolution of the structures. However, within a certain range of experimental parameters, the microstructuring of kerfs on stainless steel surfaces with a solution of $\mathrm{H}_3\mathrm{PO}_4$ shows periodic ripples, which are considered to originate from an intrinsic dynamics. The model mimics a few of the various physical and chemical processes involved and within certain parameter ranges reproduces some morphological aspects of the structures, in particular ripple regimes. We analyze the range of values of laser beam power for the appearance of ripples in both experimental and simulated kerfs. The discrete model is an extension of one that has been used previously in the context of ion sputtering and is related to a noisy version of the Kuramoto-Sivashinsky equation used extensively in the field of pattern formation.Comment: Revised version. Etching probability distribution and new simulations adde

Stationary Properties of a Randomly Driven Ising Ferromagnet

We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast switching, random external field. Analytic results for the stationary state are presented in mean-field approximation, exhibiting a novel type of first order phase transition related to dynamic freezing. Monte Carlo simulations performed on a quadratic lattice indicate that many features of the mean field theory may survive the presence of fluctuations.Comment: 5 pages in RevTex format, 7 eps/ps figures, send comments to "mailto:[email protected]", submitted to PR