The tight-binding model with correlated disorder introduced by Izrailev and Krokhin [PRL 82, 4062 (1999)] has been extended to the Kronig-Penney model. The results of the calculations have been compared with microwave transmission spectra through a single-mode waveguide with inserted correlated scatterers. All predicted bands and mobility edges have been found in the experiment, thus demonstrating that any wanted combination of transparent and non-transparent frequency intervals can be realized experimentally by introducing appropriate correlations between scatterers.PACS numbers: 72.15. Rn, 72.20.Ee, 73.20.Jc Starting from the pioneering paper by Anderson [1], a lot of progress has been achieved in the theoretical study of 1D tight-binding models. This model includes a wide range of different physical situations lying in between two limit cases: ideal periodic lattices where all states are extended, and completely random lattices where any state is exponentially localized. Specific interest has been paid to the so-called pseudo-random (or deterministic aperiodic) potentials which demonstrate either localization or delocalization, depending on their parameters [2][3][4]. A widely used model is described by the Harper equation with the site potential V n = ǫ cos(2παn). For α irrational, the incommensurability of the potential gives rise to a localization-delocalization transition (for all states) when the amplitude ǫ passes through the critical value ǫ cr = 2, see e.g., Ref. [5]. For fixed ǫ the energy spectrum of the Harper equation exhibits the famous Hofstadter butterfly [6] when α scans the interval [0, 1]. This rather exotic spectrum was recently observed experimentally [7] by making use of the equivalence of the Harper equation and the wave equation in a single-mode electromagnetic waveguide with point-like scatterers.For a long time a coexistence of localized and extended states in the spectrum of eigenenergies of 1D random potentials was considered to be impossible. However, it was shown in Refs. [8,9] that a discrete set of delocalized states appears if short-range correlations are introduced in a random potential. This is done by repeating twice each value of site potential (dimer model). Recently discrete extended states have been observed in the experiment with GaAs-AlGaAs random superlattices [10].A general case of 1D potential in tight-binding approximation with arbitrary correlations was considered in Ref. [11]. A direct relation between the pair correlation function and the localization length has been derived. This relation shows that the mobility edge does exist in 1D geometry. A few examples of potentials with correlated disorder were given. All these potentials necessarily contain the long-range correlations which thus give rise to a continuum set of delocalized states and to mobility edge.

We quantify the presence of direct processes in the S matrix of chaotic microwave cavities with absorption in the one-channel case. To this end the full distribution P(S)(S) of the S matrix, i.e., S=sqrt[R]e(itheta), is studied in cavities with time-reversal symmetry for different antenna coupling strengths T(a) or direct processes. The experimental results are compared with random-matrix calculations and with numerical simulations including absorption. The theoretical result is a generalization of the Poisson kernel. The experimental and the numerical distributions are in excellent agreement with theoretical predictions for all cases.

The concept of fidelity decay is discussed from the point of view of the scattering matrix, and the scattering fidelity is introduced as the parametric cross-correlation of a given S-matrix element, taken in the time domain, normalized by the corresponding autocorrelation function. We show that for chaotic systems, this quantity represents the usual fidelity amplitude, if appropriate ensemble and/or energy averages are taken. We present a microwave experiment where the scattering fidelity is measured for an ensemble of chaotic systems. The results are in excellent agreement with random matrix theory for the standard fidelity amplitude. The only parameter, namely the perturbation strength could be determined independently from level dynamics of the system, thus providing a parameter free agreement between theory and experiment.

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We present a microwave realization of finite tight-binding graphene-like structures. The structures are realized using disks with a high index of refraction. The disks are placed on a metallic surface while a second surface is adjusted atop the discs, such that the waves coupling the disks in the air are evanescent, leading to the tight-binding behavior. In reflection measurements the Dirac point and a linear increase close to the Dirac point is observed, if the measurement is performed inside the sample. Resonances due to edge states are found close to the Dirac point if the measurements are performed at the zigzag-edge or at the corner in case of a broken benzene ring.