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