Microwave graph analogs for the voltage drop in three-terminal devices with orthogonal, unitary, and symplectic symmetry.

Transmission measurements through three-port microwave graphs are performed, in analogy to three-terminal voltage drop devices with orthogonal, unitary, and symplectic symmetry. The terminal used as a probe is symmetrically located between two chaotic subgraphs, and each graph is connected to one port, the input and the output, respectively. The analysis of the experimental data clearly exhibits the weak localization and antilocalization phenomena. We find a good agreement with theoretical predictions, provided that the effects of dissipation and imperfect coupling to the ports are taken into account.

Phenomenological approach to transport through three-terminal disordered wires.

We study the voltage drop along three-terminal disordered wires in all transport regimes, from the ballistic to the localized regime. This is performed by measuring the voltage drop on one side of a one-dimensional disordered wire in a three-terminal setup as a function of disorder. Two models of disorder in the wire are considered: (i) the one-dimensional Anderson model with diagonal disorder and (ii) finite-width bulk-disordered waveguides. Based on the known ß dependence of the voltage drop distribution of the three-terminal chaotic case, ß being the Dyson symmetry index (ß=1, 2, and 4 for orthogonal, unitary, and symplectic symmetries, respectively), the analysis is extended to a continuous parameter ß>0 and uses the corresponding expression as a phenomenological one to reach the disordered phase. We show that our proposal encompasses all the transport regimes with ß depending linearly on the disorder strength.

Experimental evidence of coherent transport.

Coherent transport phenomena are difficult to observe due to several sources of decoherence. For instance, in the electronic transport through quantum devices the thermal smearing and dephasing, the latter induced by inelastic scattering by phonons or impurities, destroy phase coherence. In other wave systems, the temperature and dephasing may not destroy the coherence and can then be used to observe the underlying wave behaviour of the coherent phenomena. Here, we observe coherent transmission of mechanical waves through a two-dimensional elastic Sinai billiard with two waveguides. The flexural-wave transmission, performed by non-contact means, shows the quantization when a new mode becomes open. These measurements agree with the theoretical predictions of the simplest model highlighting the universal character of the transmission fluctuations.

Möbius transformations and electronic transport properties of large disorderless networks.

We show that the key transport states, insulating and conducting, of large regular networks of scatterers can be described generically by negative and zero Lyapunov exponents, respectively, of Möbius maps that relate the scattering matrix of systems with successive sizes. The conductive phase is represented by weakly chaotic attractors that have been linked with anomalous transport and ergodicity breaking. Our conclusions, verified for serial as well as parallel stub and ring structures, reveal that mesoscopic behavior results from a drastic reduction of degrees of freedom.

Wave systems with direct processes and localized losses or gains: the nonunitary Poisson kernel.

We study the scattering of waves in systems with losses or gains simulated by imaginary potentials. This is done for a complex delta potential that corresponds to a spatially localized absorption or amplification. In the Argand plane the scattering matrix moves on a circle C centered on the real axis, but not at the origin, that is tangent to the unit circle. From the numerical simulations it is concluded that the distribution of the scattering matrix, when measured from the center of the circle C, agrees with the nonunitary Poisson kernel. This result is also obtained analytically by extending the analyticity condition, of unitary scattering matrices, to the no-unitary ones. We use this nonunitary Poisson kernel to obtain the distribution of nonunitary scattering matrices when measured from the origin of the Argand plane. The obtained marginal distributions have excellent agreement with the numerical results.

Equivalence between the mobility edge of electronic transport on disorderless networks and the onset of chaos via intermittency in deterministic maps.

We exhibit a remarkable equivalence between the dynamics of an intermittent nonlinear map and the electronic transport properties (obtained via the scattering matrix) of a crystal defined on a double Cayley tree. This strict analogy reveals in detail the nature of the mobility edge normally studied near (not at) the metal-insulator transition in electronic systems. We provide an analytical expression for the conductance as a function of the system size that at the transition obeys a q-exponential form. This manifests as power-law decay or few and far between large spike oscillations according to different kinds of boundary conditions.

Absorption strength in absorbing chaotic cavities.

We derive an exact formula to calculate the absorption strength in absorbing chaotic systems such as microwave cavities or acoustic resonators. The formula allows us to estimate the absorption strength as a function of the averaged reflection coefficient and the real coupling parameter. We also define the weak and strong absorption regimes in terms of the coupling parameter and the absorption strength.

Statistical fluctuations of the parametric derivative of the transmission and reflection coefficients in absorbing chaotic cavities.

Motivated by recent theoretical and experimental works, we study the statistical fluctuations of the parametric derivative of the transmission T and reflection R coefficients, T/deltaX and R/deltaX, respectively, in ballistic chaotic cavities in the presence of absorption. Analytical results for the variance of T/deltaX and R/deltaX, with and without time-reversal symmetry, are obtained for asymmetric and left-right symmetric cavities. These results are valid for an arbitrary number of channels for strong absorption strength, in complete agreement with the results found in the literature in the absence of absorption. A simple extrapolation to any absorption strength is qualitatively correct.

Statistical wave scattering through classically chaotic cavities in the presence of surface absorption.

We propose a model to describe the statistical properties of wave scattering through a classically chaotic cavity in the presence of surface absorption. Experimentally, surface absorption could be realized by attaching an "absorbing patch" to the inner wall of the cavity. In our model, the cavity is connected to the outside by a waveguide with N open modes (or channels), while an experimental patch is simulated by an "absorbing mirror" attached to the inside wall of the cavity; the mirror, consisting of a waveguide that supports N(a) channels, with absorption inside and a perfectly reflecting wall at its end, is described by a subunitary scattering matrix S(a). The number of channels N(a) , as a measure of the geometric cross section of the mirror, and the lack of unitarity P(a) = [symbol: see text]N(a) - S(a)(+)S(a) , as a measure of absorption, are under our control: these parameters have an important physical significance for real experiments. The absorption strength in the cavity is quantified by gamma(a) = tr P(a). The statistical distribution of the resulting S matrix for N = 1 open channel and only one absorbing channel, N(a) = 1, is solved analytically for the orthogonal and unitary universality classes, beta = 1 and beta = 2, respectively, and the results are compared with those arising from numerical simulations. The relation with other models existing in the literature, in some of which absorption has a volumetric character, is also studied.

Effect of spatial reflection symmetry on the distribution of the parametric conductance derivative in ballistic chaotic cavities.

We study the effect of left-right symmetry on the distribution of the parametric derivative of the dimensionless conductance T with respect to an external parameter X , partial differentialT/ partial differentialX , of ballistic chaotic cavities with two leads, each supporting N propagating modes. We show that T and partial differentialT/ partial differentialX are linearly uncorrelated for any N . For N=1 we calculate the distribution of partial differentialT/ partial differentialX in the presence and absence of time-reversal invariance. In both cases, it has a logarithmic singularity at zero derivative and algebraic tails with an exponent different from the one of the asymmetric case. We also obtain explicit analytical results for the mean and variance of the distribution of partial differentialT/ partial differentialX for arbitrary N . Numerical simulations are performed for N=5 and 10 to show that the distribution P ( partial differentialT/ partial differentialX) tends towards a Gaussian one when N increases.

Direct processes in chaotic microwave cavities in the presence of absorption.

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.

Universal transport properties of open microwave cavities with and without time-reversal symmetry.

We measure the transmission through asymmetric and reflection-symmetric chaotic microwave cavities in dependence on the number of attached waveguides. Ferrite cylinders are placed inside the cavities to break time-reversal symmetry. The phase-breaking properties of the ferrite and its range of applicability are discussed in detail. We use the random matrix theory accounting for absorption effects to calculate the universal distribution of transmission coefficients T and their energy derivatives dT/depsilon. Using the absorption strength as a fitting parameter, we find good agreement between universal transmission fluctuations predicted by the theory and the experimental data.