Wavelet analysis on symbolic sequences and two-fold de Bruijn sequences

The concept of symbolic sequences play important role in study of complex systems. In the work we are interested in ultrametric structure of the set of cyclic sequences naturally arising in theory of dynamical systems. Aimed at construction of analytic and numerical methods for investigation of clusters we introduce operator language on the space of symbolic sequences and propose an approach based on wavelet analysis for study of the cluster hierarchy. The analytic power of the approach is demonstrated by derivation of a formula for counting of {\it two-fold de Bruijn sequences}, the extension of the notion of de Bruijn sequences. Possible advantages of the developed description is also discussed in context of applied

Accumulation effects in modulation spectroscopy with high repetition rate pulses: recursive solution of optical Bloch equations

Application of the phase modulated pulsed light for advance spectroscopic measurements is the area of growing interest. The phase modulation of the light causes modulation of the signal. Separation of the spectral components of the modulations allows to distinguish the contributions of various interaction pathways. The lasers with high repetition rate used in such experiments can lead to appearance of the accumulation effects, which become especially pronounced in systems with long-living excited states. Recently it was shown, that such accumulation effects can be used to evaluate parameters of the dynamical processes in the material. In this work we demonstrate that the accumulation effects are also important in the quantum characteristics measurements provided by modulation spectroscopy. In particular, we consider a model of quantum two-level system driven by a train of phase-modulated light pulses, organised in analogy with the 2D spectroscopy experiments. We evaluate the harmonics' amplitudes in the fluorescent signal and calculate corrections appearing from the accumulation effects. We show that the corrections can be significant and have to be taken into account at analysis of experimental data.Comment: 10 pages, 5 figure

Vibration Assisted Polariton Wavefunction Evolution in Organic Nanofibers

Formation of the composite photonic-excitonic particles, known as polaritons, is an emerging phenomenon in materials possessing strong coupling to light. The organic-based materials besides the strong light-matter interaction also demonstrate strong interaction of electronic and vibrational degrees of freedom. We utilize the Dirac-Frenkel variation principle to derive semiclassical equations for the vibration-assisted polariton wavefunction evolution when both types of interactions are treated as equally strong. By means of the approach, we study details of the polariton relaxation process and the mechanism of the polariton light emission. In particular, we propose the photon emission mechanism, which is realized when the polariton wave package exceeds the geometrical size of the nanosystem. To verify our conclusions we reproduce the fluorescence peak observed in experiment (Takazawa \textit{et.al.} Phys.Rev.Let. \textbf{105}:07401, 2010) and estimate the light-matter interaction parameter

Clustering of periodic orbits and ensembles of truncated unitary matrices

Periodic orbits in chaotic systems form clusters, whose elements traverse approximately the same points of the phase space. The distribution of cluster sizes depends on the length n of orbits and the parameter p which controls closeness of orbits actions. We show that counting of cluster sizes in the baker's map can be turned into a spectral problem for an ensemble of truncated unitary matrices. Based on the conjecture of the universality for the eigenvalues distribution at the spectral edge of these ensembles, we obtain asymptotics of the second moment of cluster distribution in a regime where both n and p tend to infinity. This result allows us to estimate the average cluster size as a function of the number of encounters in periodic orbits.Comment: 16 pages, 5 figure

The nature of relaxation processes revealed by the action signals of phase modulated light fields

We introduce a generalized theoretical approach to study action signals induced by the absorption of two-photons from two phase modulated laser beams and subject it to experimental testing for two types of photoactive samples, solution of rhodamine 6G and GaP photodiode. In our experiment, the phases of the laser beams are modulated at the frequencies f1 and f2, respectively. The action signals, such as photoluminescence and photocurrent, which result from the absorption of two photons, are isolated at frequencies m f (f=|f1-f2|, m=0,1,2...). We demonstrate that the ratio of the amplitudes of the secondary (m=2) and the primary (m=1) signals is sensitive to the type of relaxation process taken place in the system and thus can be used for its identification. Such sensitivity originates from cumulative effects of non-equilibrated state of the system between the light pulses. When the cumulative effects are small, i.e. the relaxation time is much shorter then the laser repetition rate or the laser intensity is high enough to dominate the system behavior, the ratio achieves its reference value 1:4 (the signature of two-photon absorption). In the intermediate regimes the ratio changes rapidly with the growth of intensity from zero value in case of second order relaxation process, while it demonstrates slow monotonic decrease for linear relaxation. In the article we also determine the value of the recombination rate in a GaP photodiode by using the above approach

Fluorescence correlation spectroscopy in thin films at reflecting substrates as a means to study nanoscale structure and dynamics at soft-matter interfaces

Structure and dynamics at soft-matter interfaces play an important role in nature and technical applications. Optical single-molecule investigations are non-invasive and capable to reveal heterogeneities at the nanoscale. In this work we develop an autocorrelation function (ACF) approach to retrieve tracer diffusion parameters obtained from fluorescence correlation spectroscopy (FCS) experiments in thin liquid films at reflecting substrates. This approach then is used to investigate structure and dynamics in 100 nm thick 8CB liquid crystal films on silicon wafers with five different oxide thicknesses. We find a different extension of the structural reorientation of 8CB at the solid-liquid interface for thin and for thick oxide. For the thin oxides, the perylenediimide tracer diffusion dynamics in general agrees with the hydrodynamic modeling using no-slip boundary conditions with only a small deviation close to the substrate, while a considerably stronger decrease of the interfacial tracer diffusion is found for the thick oxides.Comment: 8 figure