相关论文: Statistics and control of waves in disordered medi…
In this second chapter, we analyse transmission problems between a dielectric and a dispersive negative material. In the first part, we consider a transmission problem between two half-spaces, filled respectively by the vacuum and a Drude…
We report on experiments that were performed with microwave waveguide systems and demonstrate that in the frequency range of a single transversal mode they may serve as a model for closed and open quantum graphs. These consist of bonds that…
The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in…
Scattering on a resonance state coupled to a complicated background is a typical problem for mesoscopic quantum many-body systems as well as for wave propagation in the presence of a complex environment. On average, such a simple mode…
Epidemics-inspired techniques have received huge attention in recent years from the distributed systems and networking communities. These algorithms and protocols rely on probabilistic message replication and redundancy to ensure reliable…
This chapter is a pedagogical review of methods and results for studying wave propagation in one-dimensional complex structures. We describe and compare the tight-binding, scattering matrix, transfer matrix and Riccati formalisms. We…
We will discuss a one-dimensional approximation for the problem of wave propagation in networks of thin fibers. The main objective here is to describe the boundary (gluing) conditions at branching points of the limiting one-dimensional…
We present a statistical study of the transmission and dwell-time matrices in disordered media composed of resonators, focusing on how frequency detuning influences their eigenvalue distributions. Our analysis reveals that the distribution…
In a recent letter [Europhys. Lett. 97, 34002 (2012)], random matrix theory is introduced for long-range acoustic propagation in the ocean. The theory is expressed in terms of unitary propagation matrices that represent the scattering…
The nature of transport of electrons and classical waves in disordered systems depends upon the proximity to the Anderson localization transition between freely diffusing and localized waves. The suppression of average transport and the…
We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
The probability distribution of the proper delay times during scattering on a chaotic system is derived in the framework of the random matrix approach and the supersymmetry method. The result obtained is valid for an arbitrary number of…
In this work we have studied the optical properties of disordered photonic structures, in which we have controlled the distribution of the random layer thickness. Such structures are characterized by an alternation of high and low…
We realized one dimensional disordered photonic structures by grouping high refractive index layers in clusters, randomly distributed in such structure. We have control on the maximum size of the cluster and on the ratio high-low refractive…
It is described how one comes to the Wigner-Dyson random matrix theory (RMT) starting from a model of a disordered metal. The lectures start with a historical introduction where basic ideas of the RMT and theory of disordered metals are…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
Wave localization is a ubiquitous phenomenon. It refers to situations that transmitted waves in scattering media are trapped in space and remain confined in the vicinity of the initial site until dissipated. Based on a scaling analysis, the…
We analyse the single-mode transmission of microwaves in a guide with internal random structure. The waveguide contains scatterers characterised by random heights and positions, corresponding to compositional and structural disorder. We…
A one-dimensional quantum system with off diagonal disorder, consisting of a sample of conducting regions randomly interspersed within potential barriers is considered. Results mainly concerning the large $N$ limit are presented. In…
The propagation of waves in highly inhomogeneous media is a problem of interest in multiple fields including seismology, acoustics and electromagnetism. It is also relevant for technological applications such as the design of sound…