M. Martínez-Mares

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.

Electromagnetic prompt response in an elastic wave cavity

A. M. Mart́ınez-Argüello, M. Mart́ınez-Mares, M. Cobián-Suárez, G. Báez, and R. A. Méndez-Sánchez Departamento de F́ısica, Universidad Autónoma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340 México Distrito Federal, Mexico Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana-Azcapotzalco, Apartado Postal 21-267, 04000 México Distrito Federal, Mexico Instituto de Ciencias F́ısicas, Universidad Nacional Autónoma de México, Apartado Postal 48-3, 62210 Cuernavaca Mor., MexicoIn a wave resonant scattering process the interference of the continuous scattering amplitude with a discrete resonant state, both of the same undulatory nature, gives rise to a Fano resonance profile. We report experimental evidence of a new kind of Fano resonance, in which the continuous amplitude is of a different nature than that of the resonant wave. The continuous amplitude, of a electromagnetic nature, comes from the measurement process and induces a new type of prompt, or rapid, response of the system which we describe theoretically including this response as a direct process.

A new Fano resonance in measurement processes

A. M. Mart́ınez-Argüello, M. Mart́ınez-Mares, M. Cobián-Suárez, G. Báez, and R. A. Méndez-Sánchez Departamento de F́ısica, Universidad Autónoma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340 México Distrito Federal, Mexico Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana-Azcapotzalco, Apartado Postal 21-267, 04000 México Distrito Federal, Mexico Instituto de Ciencias F́ısicas, Universidad Nacional Autónoma de México, Apartado Postal 48-3, 62210 Cuernavaca Mor., MexicoIn a wave resonant scattering process the interference of the continuous scattering amplitude with a discrete resonant state, both of the same undulatory nature, gives rise to a Fano resonance profile. We report experimental evidence of a new kind of Fano resonance, in which the continuous amplitude is of a different nature than that of the resonant wave. The continuous amplitude, of a electromagnetic nature, comes from the measurement process and induces a new type of prompt, or rapid, response of the system which we describe theoretically including this response as a direct process.

Random matrix study for a three-terminal chaotic device

We perform a study based on a random-matrix theory simulation for a three-terminal device, consisting of chaotic cavities on each terminal. We analyze the voltage drop along one wire with two chaotic mesoscopic cavities, connected by a perfect conductor, or waveguide, with one open mode. This is done by means of a probe, which also consists of a chaotic cavity that measure the voltage in different configurations. Our results show significant differences with respect to the disordered case, previously considered in the literature.

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.

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.

Absorption and Direct Processes in Chaotic Wave Scattering

Recent results on the scattering of waves by chaotic systems with losses and direct processes are discussed. We start by showing the results without direct processes nor absorption. We then discuss systems with direct processes and lossy systems separately. Finally the discussion of systems with both direct processes and loses is given. We will see how the regimes of strong and weak absorption are modified by the presence of the direct processes.