arXiv subjects

M. Martínez-Mares

Publications and source records attributed to M. Martínez-Mares.

16 recordsLinked to original sources

arXiv2024

Thermal transport of flexural phonons in a rectangular wire

We study the quantum thermal transport of elastic excitations through a two-dimensional elastic waveguide between two thermal reservoirs. We solve the classical Kirchhoff-Love equation for rectangular wires and explore the dispersion relation for both the symmetric and antisymmetric solutions. Then, we study the phonon transport of these modes within the second quantization framework by analyzing the mean quadratic displacement, from which the energy density current, the temperature field, and conductance are determined. We identify the relevant modes contributing to thermal transport and explore the average temperature difference to reach the high-temperature limit. We expect our results to pave the way for understanding phonon-mediated thermal transport in two-dimensional mesoscopic quantum devices.

cond-mat.mes-hall↗

arXiv2021

Microwave graphs 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 a symmetric setting, 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 graphs, each graph is connected to one port, the input and the output, respectively. The analysis of the experimental data exhibit the weak localization and antilocalization phenomena in a clear fashion. We find a good agreement with theoretical predictions, provided that the effect of dissipation and imperfect coupling to the ports are taken into account.

cond-mat.other↗

arXiv2019

Experimental validation of the theoretical prediction for the optical $S$ matrix

Scattering of waves is omnipresent in nature in systems with sizes varying from $10^{-15}$ to $10^{25}$ m. Within this 40 orders of magnitude, in a great number of systems, the scattering can be separated in an averaged response that crosses rapidly the scattering region and a fluctuating delayed response. This fact is the basis of the optical model; the averaged response, represented by the optical matrix $\langle S\rangle$, is composed with the fluctuating part that can be taken as a random matrix. Although the optical model was developed more than 60 years ago, a theoretical prediction for the optical matrix was obtained until very recently. The validity of such prediction is experimentally demonstrated here. This is done studying the scattering of torsional waves in a quasi-1D elastic system in which a locally periodic system is built; the distribution of the scattering matrix is calculated completely free of parameters. In contradistinction to all previous works, in microwaves and in elasticity, in which the value of $\langle S\rangle$ is obtained from the experiment, here the theoretical prediction is used to compare with the experiment. Numerical simulations show that the theoretical value is still valid when strong disorder is present. Several applications of the theoretical expression for the optical matrix in other areas of physics are proposed. Possible extensions of this work are also discussed.

cond-mat.dis-nn↗

arXiv2018

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 set-up 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 $β$-dependence of the voltage drop distribution of the three-terminal chaotic case, being $β$ the Dyson symmetry index ($β=1$, 2, and 4 for orthogonal, unitary, and symplectic symmetries, respectively), the analysis is extended to a continuous parameter $β>0$ and use the corresponding expression as a phenomenological one to reach the disordered phase. We show that our proposal encompasses all the transport regimes with $β$ depending linearly on the disorder strength.

cond-mat.mes-hall↗

arXiv2018

Transport studies in three-terminal microwave graphs with orthogonal, unitary, and symplectic symmetry

The Landauer-Büttiker formalism establishes an equivalence between the electrical conduction through a device, e.g., a quantum dot, and the transmission. Guided by this analogy we perform transmission measurements through three-port microwave graphs with orthogonal, unitary, and symplectic symmetry thus mimicking three-terminal voltage drop devices. One of the ports is placed as input and a second one as output, while a third port is used as a probe. Analytical predictions show good agreement with the measurements in the presence of orthogonal and unitary symmetries, provided that the absorption and the influence of the coupling port are taken into account. The symplectic symmetry is realized in specifically designed graphs mimicking spin 1/2 systems. Again a good agreement between experiment and theory is found. For the symplectic case the results are marginally sensitive to absorption and coupling strength of the port, in contrast to the orthogonal and unitary case.

cond-mat.mes-hall↗

arXiv2017

Analytical prediction for the optical matrix

Contrary to praxis, we provide an analytical expression, for a physical locally periodic structure, of the average $\langle S\rangle$ of the scattering matrix, called optical $S$ matrix in the nuclear physics jargon, and fundamentally present in all scattering processes. This is done with the help of a strictly analogous nonlinear dynamical mapping where iteration time is the number $N$ of scatterers. The ergodic property of chaotic attractors implies the existence and analyticity of $\langle S\rangle$. We find that the optical $S$ matrix depends only on the transport properties of a single cell, and that the Poisson kernel is the distribution of the scattering matrix $S_N$ in the large size limit $N\rightarrow \infty$. The theoretical distribution shows perfect agreement with numerical results for a chain of delta potentials. A consequence of our findings is the a priori knowledge of $\langle S\rangle$ without resort to experimental data.

cond-mat.stat-mech↗

arXiv2016

Typical length scales in conducting disorderless networks

We take advantage of a recently established equivalence, between the intermittent dynamics of a deterministic nonlinear map and the scattering matrix properties of a disorderless double Cayley tree lattice of connectivity $K$, to obtain general electronic transport expressions and expand our knowledge of the scattering properties at the mobility edge. From this we provide a physical interpretation of the generalized localization length.

cond-mat.dis-nn↗

arXiv2015

Delay times in chaotic quantum systems

By an inductive reasoning, and based on recent results of the joint moments of proper delay times of open chaotic systems for ideal coupling to leads, we obtain a general expression for the distribution of the partial delay times for an arbitrary number of channels and any symmetry. This distribution was not completely known for all symmetry classes. Our theoretical distribution is verified by random matrix theory simulations of ballistic chaotic cavities.

cond-mat.mes-hall↗

arXiv2015

Testing quantum transport without decoherence

The coherent electronic transport phenomena through quantum devices is difficult to observe due to thermal smearing and dephasing, the latter induced by inelastic scattering by phonons or impurities. 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 quantum 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 transmission quantization when a new mode becomes open. In contrast with the quantum counterpart, these measurements agree with the theoretical predictions of the simplest model at zero temperature highlighting the universal character of the transmission fluctuations.

cond-mat.mtrl-sci↗

arXiv2015

Electromagnetic prompt response in an elastic wave cavity

A rapid, or prompt response, of an electromagnetic nature, is found in an elastic wave scattering experiment. The experiment is performed with torsional elastic waves in a quasi-one-dimensional cavity with one port, formed by a notch grooved at a certain distance from the free end of a beam. The stationary patterns are diminished using a passive vibration isolation system at the other end of the beam. The measurement of the resonances is performed with non-contact electromagnetic-acoustic transducers outside the cavity. In the Argand plane, each resonance describes a circle over a base impedance curve which comes from the electromagnetic components of the equipment. A model, based on a variation of Poisson's kernel is developed. Excellent agreement between theory and experiment is obtained.

nlin.CD↗

arXiv2014

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.

cond-mat.mes-hall↗

arXiv2013

Scattering of Elastic Waves in a Quasi-one-dimensional Cavity: Theory and Experiment

We study the scattering of torsional waves through a quasi-one-dimensional cavity both, from the experimental and theoretical points of view. The experiment consists of an elastic rod with square cross section. In order to form a cavity, a notch at a certain distance of one end of the rod was grooved. To absorb the waves, at the other side of the rod, a wedge, covered by an absorbing foam, was machined. In the theoretical description, the scattering matrix S of the torsional waves was obtained. The distribution of S is given by Poisson's kernel. The theoretical predictions show an excellent agreement with the experimental results. This experiment corresponds, in quantum mechanics, to the scattering by a delta potential, in one dimension, located at a certain distance from an impenetrable wall.

cond-mat.mes-hall↗

arXiv2012

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.

cond-mat.mes-hall↗

arXiv2012

Wave systems with direct processes and localized losses or gains: the non-unitary 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 non-unitary Poisson kernel. This result is also obtained analytically by extending the analyticity condition, of unitary scattering matrices, to the non-unitary ones. We use this non-unitary Poisson kernel to obtain the distribution of non-unitary scattering matrices when measured from the origin of the Argand plane. The obtained marginal distributions have an excellent agreement with the numerical results.

cond-mat.mes-hall↗

arXiv2011

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.

cond-mat.mes-hall↗

arXiv2011

Scattering matrix of elliptically polarized waves

We analyze the scattering of elliptically polarized plane waves normally incident at the planar interface between two different materials; we consider two cases: dielectric-dielectric and dielectric-conductor interfaces. The scattering matrix S in both cases is obtained using the boundary conditions and Poynting's theorem. In the dielectric-dielectric case we write S using two different basis, the usual xy and a rotated one. For the dielectric-conductor interface, the use of the rotated basis together with an energy balance argument leads us, in a natural way, to construct a unitary S matrix after recognizing the need to introduce two equivalent parasitic channels due to dissipation in the conductor, and the transmission coefficient into these parasitic channels measures the absorption strength.

physics.class-ph↗