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J. A. Mendez-Bermudez

Publications and source records attributed to J. A. Mendez-Bermudez.

48 records · Page 3Linked to original sources
arXiv2010

Scattering and transport statistics at criticality

We study numerically scattering and transport statistical properties of the one-dimensional Anderson model at the metal-insulator transition described by the Power-law Banded Random Matrix (PBRM) model at criticality. Within a scattering approach to electronic transport, we concentrate on the case of a small number of single-channel attached leads. We observe a smooth transition from localized to delocalized behavior in the average scattering matrix elements, the conductance probability distribution, the variance of the conductance, and the shot noise power by varying $b$ (the effective bandwidth of the PBRM model) from small ($b\ll 1$) to large ($b>1$) values. We contrast our results with analytic random matrix theory predictions which are expected to be recovered in the limit $b\to \infty$. We also compare our results for the PBRM model with those for the three-dimensional (3D) Anderson model at criticality, finding that the PBRM model with $b \in [0.2,0.4]$ reproduces well the scattering and transport properties of the 3D Anderson model.

cond-mat.dis-nn↗
arXiv2009

Quantum Scattering and Transport in Classically Chaotic Cavities: An Overview of Past and New Results

We develop a statistical theory that describes quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynamics is chaotic. This picture is relevant to a variety of physical systems, ranging from atomic nuclei to mesoscopic systems and microwave cavities; the main application to be discussed in this contribution is to electronic transport through mesoscopic ballistic structures or quantum dots. The theory describes the regime in which there are two distinct time scales, associated with a prompt and an equilibrated response, and is cast in terms of the matrix of scattering amplitudes S. We construct the ensemble of S matrices using a maximum-entropy approach which incorporates the requirements of flux conservation, causality and ergodicity, and the system-specific average of S which quantifies the effect of prompt processes. The resulting ensemble, known as Poisson's kernel, is meant to describe those situations in which any other information is irrelevant. The results of this formulation have been compared with the numerical solution of the Schroedinger equation for cavities in which the assumptions of the theory hold. The model has a remarkable predictive power: it describes statistical properties of the quantum conductance of quantum dots, like its average, its fluctuations, and its full distribution in several cases. We also discuss situations that have been found recently, in which the notion of stationarity and ergodicity is not fulfilled, and yet Poisson's kernel gives a good description of the data. At the present moment we are unable to give an explanation of this fact.

cond-mat.mes-hall↗
arXiv2009

Effects of Andreev reflection on the conductance of quantum-chaotic dots

We investigate the conductance statistics of a quantum-chaotic dot--a normal-metal grain--with a superconducting lead attached to it. The cases of one and two normal leads additionally attached to the dot are studied. For these two configurations the complete distribution of the conductance is calculated, within the framework of random matrix theory, as a function of the transparency parameter of the Schottky barrier formed at the interface of the normal-metal and superconducting regions. Our predictions are verified by numerical simulations.

cond-mat.mes-hall↗
arXiv2007

Scaling properties of delay times in one-dimensional random media

The scaling properties of the inverse moments of Wigner delay times are investigated in finite one-dimensional (1D) random media with one channel attached to the boundary of the sample. We find that they follow a simple scaling law which is independent of the microscopic details of the random potential. Our theoretical considerations are confirmed numerically for systems as diverse as 1D disordered wires and optical lattices to microwave waveguides with correlated scatterers.

cond-mat.dis-nn↗
arXiv2006

Scattering at the Anderson transition: Power--law banded random matrix model

We analyze the scattering properties of a periodic one-dimensional system at criticality represented by the so-called power-law banded random matrix model at the metal insulator transition. We focus on the scaling of Wigner delay times $τ$ and resonance widths $Γ$. We found that the typical values of $τ$ and $Γ$ (calculated as the geometric mean) scale with the system size $L$ as $τ^{\tiny typ}\propto L^{D_1}$ and $Γ^{\tiny typ} \propto L^{-(2-D_2)}$, where $D_1$ is the information dimension and $D_2$ is the correlation dimension of eigenfunctions of the corresponding closed system.

cond-mat.dis-nn↗
arXiv2006

Parametric invariant Random Matrix Model and the emergence of multifractality

We propose a random matrix modeling for the parametric evolution of eigenstates. The model is inspired by a large class of quantized chaotic systems. Its unique feature is having parametric invariance while still possessing the non-perturbative crossover that has been discussed by Wigner 50 years ago. Of particular interest is the emergence of an additional crossover to multifractality.

cond-mat.mes-hall↗
arXiv2005

Resonance width distribution for high-dimensional random media

We study the distribution of resonance widths P(G) for three-dimensional (3D) random scattering media and analyze how it changes as a function of the randomness strength. We are able to identify in P(G) the system-inherent fingerprints of the metallic, localized, and critical regimes. Based on the properties of resonance widths, we also suggest a new criterion for determining and analyzing the metal-insulator transition. Our theoretical predictions are verified numerically for the prototypical 3D tight-binding Anderson model.

cond-mat.dis-nn↗
arXiv2005

Design of beam splitters and microlasers using chaotic waveguides

We consider waveguides formed by single or multiple two-dimensional chaotic cavities connected to leads. The cavities are chaotic in the sense that the ray (or equivalently, classical particle) dynamics within them is chaotic. Geometrical parameters are chosen to produce a mixed phase space (chaotic regions surrounding islands of stability where motion is regular). Incoming rays (or particles) cannot penetrate into these islands but incoming plane waves dynamically tunnel into them at a certain discrete set of frequencies (energies). The support of the corresponding quasi-bound states is along the trajectories of periodic orbits trapped within the cavity. We take advantage of this difference in the ray/wave behavior to demonstrate how chaotic waveguides can be used to design beam splitters and microlasers. We also present some preliminary experimental results in a microwave realization of such chaotic waveguide.

physics.optics↗
arXiv2005

Design of switches and beam splitters using chaotic cavities

We propose the construction of electromagnetic (or electronic) switches and beam splitters using chaotic two-dimensional multi-port waveguides. A prototype two-port waveguide is locally deformed in order to produce a ternary incomplete horseshoe proper of mixed phase space (chaotic regions surrounding islands of stability where motion is regular). Due to tunneling to the phase space stability islands the appearance of quasi-bound states (QBS) is induced. Then, we attach transversal ports to the waveguide on the deformation region in positions where the phase space structure is only slightly perturbed. We show how QBS can be guided out of the waveguide through the attached transversal ports giving rise to frequency selective switches and beam splitters.

physics.optics↗
arXiv2005

Probing the eigenfunction fractality with a stop watch

We study numerically the distribution of scattering phases ${\cal P}(Φ)$ and of Wigner delay times ${\cal P}(τ_W)$ for the power-law banded random matrix (PBRM) model at criticality with one channel attached to it. We find that ${\cal P}(Φ)$ is insensitive to the position of the channel and undergoes a transition towards uniformity as the bandwidth $b$ of the PBRM model increases. The inverse moments of Wigner delay times scale as $<τ_W^{-q} >\sim L^{- q D_{q+1}}$, where $D_q$ are the multifractal dimensions of the eigenfunctions of the corresponding closed system and $L$ is the system size. The latter scaling law is sensitive to the position of the channel.

cond-mat.mes-hall↗
arXiv2005

The twilight zone in the parametric evolution of eigenstates: beyond perturbation theory and semiclassics

Considering a quantized chaotic system, we analyze the evolution of its eigenstates as a result of varying a control parameter. As the induced perturbation becomes larger, there is a crossover from a perturbative to a non-perturbative regime, which is reflected in the structural changes of the local density of states. For the first time the {\em full} scenario is explored for a physical system: an Aharonov-Bohm cylindrical billiard. As we vary the magnetic flux, we discover an intermediate twilight regime where perturbative and semiclassical features co-exist. This is in contrast with the {\em simple} crossover from a Lorentzian to a semicircle line-shape which is found in random-matrix models.

cond-mat.mes-hall↗