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G. A. Luna-Acosta

Publications and source records attributed to G. A. Luna-Acosta.

17 recordsLinked to original sources
arXiv2016

Cross section versus time delay and trapping probability

We study the behavior of the $s$-wave partial cross section $σ(k)$, the Wigner-Smith time delay $τ(k)$, and the trapping probability $P(k)$ as function of the wave number $k$. The $s$-wave central square well is used for concreteness, simplicity, and to elucidate the controversy whether it shows true resonances. It is shown that, except for very sharp structures, the resonance part of the cross section, the trapping probability, and the time delay, reach their local maxima at different values of $k$. We show numerically that $τ(k)>0$ at its local maxima, occuring just before the resonant part of the cross section reaches its local maxima. These results are discussed in the light of the standard definition of resonance.

quant-ph↗
arXiv2009

One-Dimensional Kronig-Penney Model with Positional Disorder: Theory versus Experiment

We study the effects of random positional disorder in the transmission of waves in a 1D Kronig-Penny model. For weak disorder we derive an analytical expression for the localization length and relate it to the transmission coefficient for finite samples. The obtained results describe very well the experimental frequency dependence of the transmission in a microwave realization of the model. Our results can be applied both to photonic crystals and semiconductor super lattices.

cond-mat.dis-nn↗
arXiv2008

Impurity effects on the band structure of one-dimensional photonic crystals: Experiment and theory

We study the effects of single impurities on the transmission in microwave realizations of the photonic Kronig-Penney model, consisting of arrays of Teflon pieces alternating with air spacings in a microwave guide. As only the first propagating mode is considered, the system is essentially one dimensional obeying the Helmholtz equation. We derive analytical closed form expressions from which the band structure, frequency of defect modes, and band profiles can be determined. These agree very well with experimental data for all types of single defects considered (e.g. interstitial, substitutional) and shows that our experimental set-up serves to explore some of the phenomena occurring in more sophisticated experiments. Conversely, based on the understanding provided by our formulas, information about the unknown impurity can be determined by simply observing certain features in the experimental data for the transmission. Further, our results are directly applicable to the closely related quantum 1D Kronig-Penney model.

physics.optics↗
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↗
arXiv2003

From Chaos to Disorder in Quasi-1D Billiards with Corrugated Surfaces

We study chaotic properties of eigenstates depending on the degree of complexity in boundaries of a 2D periodic billiard. Main attention is paid to the situation when the motion of a classical particle is strongly chaotic. Our approach allows to explore the transition from deterministic to disordered chaos, and to link chaos to the degree of ergodicity in eigenstates of the billiard. We have found that bouncing balls strongly reduce chaotic properties of eigenstates, thus leading to a serious problem in statistical description for global properties of eigenstates. A quite unexpected effect of rough surfaces on the form of eigenstates has been discovered and explained by a strong localization of a subset of eigenstates in the energy representation.

cond-mat↗
arXiv2003

Amplitude and Gradient Scattering in Waveguides with Corrugated Surfaces

We study chaotic properties of eigenstates for periodic quasi-1D waveguides with "regular" and "random" surfaces. Main attention is paid to the role of the so-called "gradient scattering" which is due to large gradients in the scattering walls. We demonstrate numerically and explain theoretically that the gradient scattering can be quite strong even if the amplitude of scattering profiles is very small in comparison with the width of waveguides.

cond-mat.dis-nn↗
arXiv2003

Ballistic Localization in Quasi-1D Waveguides with Rough Surfaces

Structure of eigenstates in a periodic quasi-1D waveguide with a rough surface is studied both analytically and numerically. We have found a large number of "regular" eigenstates for any high energy. They result in a very slow convergence to the classical limit in which the eigenstates are expected to be completely ergodic. As a consequence, localization properties of eigenstates originated from unperturbed transverse channels with low indexes, are strongly localized (delocalized) in the momentum (coordinate) representation. These eigenstates were found to have a quite unexpeted form that manifests a kind of "repulsion" from the rough surface. Our results indicate that standard statistical approaches for ballistic localization in such waveguides seem to be unappropriate.

cond-mat.dis-nn↗
arXiv2003

Chaotic Waveguide-Based Resonators for Microlasers

We propose the construction of highly directional emission microlasers using two-dimensional high-index semiconductor waveguides as {\it open} resonators. The prototype waveguide is formed by two collinear leads connected to a cavity of certain shape. The proposed lasing mechanism requires that the shape of the cavity yield mixed chaotic ray dynamics so as to have the appropiate (phase space) resonance islands. These islands allow, via Heisenberg's uncertainty principle, the appearance of quasi bound states (QBS) which, in turn, propitiate the lasing mechanism. The energy values of the QBS are found through the solution of the Helmholtz equation. We use classical ray dynamics to predict the direction and intensity of the lasing produced by such open resonators for typical values of the index of refraction.

cond-mat.mes-hall↗
arXiv2002

Directional Emission from Microlasers with Open Chaotic Resonators

Using topological classical considerations (Poincarè Maps) the appearance of ``bow-tie''-shaped resonances is predicted for certain types of waveguides. The geometry of such waveguides is chosen to yield mixed chaotic dymnamics. Then, based on resonance effects, we propose the construction of directional emission microlasers using {\it open} chaotic semiconductor resonators of high refractive index.

cond-mat↗
arXiv2002

Understanding quantum scattering properties in terms of purely classical dynamics. 2D open chaotic billiards

We study classical and quantum scattering properties in the ballistic regime of particles in two-dimensional chaotic billiards that are models of electron- or micro- waveguides. To this end we construct the purely classical counterparts of the Scattering Probability (SP) matrix $\mid S_{n,m}\mid^2$ and Husimi distributions and specialize to the case of mixed chaotic motion. Comparison between classical and quantum quantities allows us to discover the purely classical dynamical origin of certain general, as well as particular features that appear in the quantum description of the system. On the other hand, at certain values of energy the tunneling of the wavefunction into classically forbidden regions produces striking differences between the classical and quantum quantities. We also see the manifestation of Whispering Gallery Orbits as a self-similar structure in the transmission part of the classical SP matrix. A potential application of this phenomenom in the field of microlasers is discussed briefly.

cond-mat.dis-nn↗
arXiv2001

Chaotic Electron Motion in Superlattices. Quantum-Classical Correspondence of the Structure of Eigenstates and LDOS

We investigate the classical-quantum correspondence for particle motion in a superlattice in the form of a 2D channel with periodic modulated boundaries. Its classical dynamics undergoes the generic transition to chaos of Hamiltonian systems as the amplitude of the modulation is increased. We show that for strong chaotic motion, the classical counterpart of the structure of eigenstates (SES) in energy space reveals an excellent agreement with the quantum one. This correspondence allows us to understand important features of the SES in terms of classical trajectories. We also show that for typical 2D modulated waveguides there exist, at any energy range, extremely localized eigenstates (in energy) which are practically unperturbed by the modulation. These states contribute to the strong fluctuations around the classical SES. The approach to the classical limit is discussed.

cond-mat.dis-nn↗
arXiv2001

Classical versus Quantum Structure of the Scattering Probability Matrix. Chaotic wave-guides

The purely classical counterpart of the Scattering Probability Matrix (SPM) $\mid S_{n,m}\mid^2$ of the quantum scattering matrix $S$ is defined for 2D quantum waveguides for an arbitrary number of propagating modes $M$. We compare the quantum and classical structures of $\mid S_{n,m}\mid^2$ for a waveguide with generic Hamiltonian chaos. It is shown that even for a moderate number of channels, knowledge of the classical structure of the SPM allows us to predict the global structure of the quantum one and, hence, understand important quantum transport properties of waveguides in terms of purely classical dynamics. It is also shown that the SPM, being an intensity measure, can give additional dynamical information to that obtained by the Poincarè maps.

cond-mat.dis-nn↗
arXiv2001

Periodic Chaotic Billiards: Quantum-Classical Correspondence in Energy Space

We investigate the properties of eigenstates and local density of states (LDOS) for a periodic 2D rippled billiard, focusing on their quantum-classical correspondence in energy representation. To construct the classical counterparts of LDOS and the structure of eigenstates (SES), the effects of the boundary are first incorporated (via a canonical transformation) into an effective potential, rendering the one-particle motion in the 2D rippled billiard equivalent to that of two-interacting particles in 1D geometry. We show that classical counterparts of SES and LDOS in the case of strong chaotic motion reveal quite a good correspondence with the quantum quantities. We also show that the main features of the SES and LDOS can be explained in terms of the underlying classical dynamics, in particular of certain periodic orbits. On the other hand, statistical properties of eigenstates and LDOS turn out to be different from those prescribed by random matrix theory. We discuss the quantum effects responsible for the non-ergodic character of the eigenstates and individual LDOS that seem to be generic for this type of billiards with a large number of transverse channels.

cond-mat.mes-hall↗
arXiv2001

Chaotic Classical Scattering and Dynamics in Oscillating 1-D Potential Wells

We study the motion of a classical particle interacting with one, two, and finally an infinite chain of 1D square wells with oscillating depth. For a single well we find complicated scattering behavior even though there is no topological chaos due to the absence of hyperbolic periodic orbits. In contrast, for two coupled square wells there is chaotic scattering. The infinite oscillating chain yields the generic transition to chaos, with diffusion in energy and in space, as the separation between wells is increased. We briefly discuss the relevance of our results to solid state physics.

nlin.CD↗
arXiv2000

An explanation of the "negative neutrino mass squared" anomaly in tritium $ β$-decay based on a theory of mass

A proposed solution of the anomalous behavior of the electron spectrum near the endpoint of tritium $β$-decay is offered. It is based on a new theory of mass in which mass becomes a dynamical variable, and the electron in the tritium $β$-decay has a narrow mass distribution. The predicted Kurie plots explain the main feature (``$m_ν^2 < 0 $'') of this anomalous behavior.

hep-ph↗
arXiv1998

Quantum weak chaos in a degenerate system

Quantum weak chaos is studied in a perturbed degenerate system --- a charged particle interacting with a monochromatic wave in a transverse magnetic field. The evolution operator for an arbitrary number of periods of the external field is built and its structure is explored in terms of the QE (quasienergy eigenstates) under resonance condition (wave frequency $=$ cyclotron frequency) in the regime of weak classical chaos. The new phenomenon of diffusion via the quantum separatrices and the influence of chaos on diffusion are investigated and, in the quasi classical limit, compared with its classical dynamics. We determine the crossover from purely quantum diffusion to a diffusion which is the quantum manifestation of classical diffusion along the stochastic web. This crossover results from the non-monotonic dependence of the characteristic localization length of the QE states on the wave amplitude. The width of the quantum separatrices was computed and compared with the width of the classical stochastic web. We give the physical parameters which can be realized experimentally to show the manifestation of quantum chaos in nonlinear acoustic resonance.

chao-dyn↗