From chaos to disorder: Statistics of the eigenfunctions of microwave cavities

We study the statistics of the experimental eigenfunctions of chaotic and disordered microwave billiards in terms of the moments of their spatial distributions, such as the Inverse Participation Ratio (IPR) and density-density auto-correlation. A path from chaos to disorder is described in terms of increasing IPR. In the chaotic, ballistic limit, the data correspond well with universal results from random matrix theory. Deviations from universal distributions are observed due to disorder induced localization, and for the weakly disordered case the data are well-described by including finite conductance and mean free path contributions in the framework of nonlinear sigma models of supersymetry.Comment: 5 pages + 2 JPG figure

Transport and dynamics on open quantum graphs

We study the classical limit of quantum mechanics on graphs by introducing a Wigner function for graphs. The classical dynamics is compared to the quantum dynamics obtained from the propagator. In particular we consider extended open graphs whose classical dynamics generate a diffusion process. The transport properties of the classical system are revealed in the scattering resonances and in the time evolution of the quantum system.Comment: 42 pages, 13 figures, submitted to PR

Classical dynamics on graphs

We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator which generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined for the time-continuous classical dynamics on graphs. These properties are given as the zeros of some periodic-orbit zeta functions. We consider in detail the case of infinite periodic graphs where the particle undergoes a diffusion process. The infinite spatial extension is taken into account by Fourier transforms which decompose the observables and probability densities into sectors corresponding to different values of the wave number. The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a Frobenius-Perron operator corresponding to a given sector. The diffusion coefficient is obtained from the hydrodynamic modes of diffusion and has the Green-Kubo form. Moreover, we study finite but large open graphs which converge to the infinite periodic graph when their size goes to infinity. The lifetime of the particle on the open graph is shown to correspond to the lifetime of a system which undergoes a diffusion process before it escapes.Comment: 42 pages and 8 figure

Periodic orbit spectrum in terms of Ruelle--Pollicott resonances

Fully chaotic Hamiltonian systems possess an infinite number of classical solutions which are periodic, e.g. a trajectory ``p'' returns to its initial conditions after some fixed time tau_p. Our aim is to investigate the spectrum tau_1, tau_2, ... of periods of the periodic orbits. An explicit formula for the density rho(tau) = sum_p delta (tau - tau_p) is derived in terms of the eigenvalues of the classical evolution operator. The density is naturally decomposed into a smooth part plus an interferent sum over oscillatory terms. The frequencies of the oscillatory terms are given by the imaginary part of the complex eigenvalues (Ruelle--Pollicott resonances). For large periods, corrections to the well--known exponential growth of the smooth part of the density are obtained. An alternative formula for rho(tau) in terms of the zeros and poles of the Ruelle zeta function is also discussed. The results are illustrated with the geodesic motion in billiards of constant negative curvature. Connections with the statistical properties of the corresponding quantum eigenvalues, random matrix theory and discrete maps are also considered. In particular, a random matrix conjecture is proposed for the eigenvalues of the classical evolution operator of chaotic billiards

Quantum fingerprints of classical Ruelle-Pollicot resonances

N-disk microwave billiards, which are representative of open quantum systems, are studied experimentally. The transmission spectrum yields the quantum resonances which are consistent with semiclassical calculations. The spectral autocorrelation of the quantum spectrum is shown to be determined by the classical Ruelle-Pollicot resonances, arising from the complex eigenvalues of the Perron-Frobenius operator. This work establishes a fundamental connection between quantum and classical correlations in open systems.Comment: 6 pages, 2 eps figures included, submitted to PR

Photonic molecules and spectral engineering

This chapter reviews the fundamental optical properties and applications of pho-tonic molecules (PMs) - photonic structures formed by electromagnetic coupling of two or more optical microcavities (photonic atoms). Controllable interaction between light and matter in photonic atoms can be further modified and en-hanced by the manipulation of their mutual coupling. Mechanical and optical tunability of PMs not only adds new functionalities to microcavity-based optical components but also paves the way for their use as testbeds for the exploration of novel physical regimes in atomic physics and quantum optics. Theoretical studies carried on for over a decade yielded novel PM designs that make possible lowering thresholds of semiconductor microlasers, producing directional light emission, achieving optically-induced transparency, and enhancing sensitivity of microcavity-based bio-, stress- and rotation-sensors. Recent advances in material science and nano-fabrication techniques make possible the realization of optimally-tuned PMs for cavity quantum electrodynamic experiments, classical and quantum information processing, and sensing.Comment: A review book chapter: 29 pages, 19 figure

Crystallographic snapshots of the interplay between reactive guest and host molecules in a porous coordination polymer: Stereochemical coupling and feedback mechanism of three photoactive centers triggered by UV-induced isomerization, dimerization, and po

We carried out photopolymerization by [2 + 2] dimerization of a photoreactive guest molecule in the channels of a photoreactive porous coordination polymer. The photoreactions of the guest and two host ligands were monitored by single-crystal X-ray crystallography, providing snapshots of the interplay between the reactive centers. By correlating the structures of these three photocenters, a strong synergism was discovered among three reaction (quasi)equilibria and three types of photochemical reactions (isomerization, dimerization, and polymerization). This result indicates a strong coupling and feedback mechanism among the photocenters moderated by the coordination backbone. ? 2013 American Chemical Society