arXiv subjects

R. A. Mendez-Sanchez

Publications and source records attributed to R. A. Mendez-Sanchez.

14 recordsLinked to original sources

arXiv2013

Anderson Localization Phenomenon in One-dimensional Elastic Systems

The phenomenon of Anderson localization of waves in elastic systems is studied. We analyze this phenomenon in two different set of systems: disordered linear chains of harmonic oscillators and disordered rods which oscillate with torsional waves. The first set is analyzed numerically whereas the second one is studied both experimentally and theoretically. In particular, we discuss the localization properties of the waves as a function of the frequency. In doing that we have used the inverse participation ratio, which is related to the localization length. We find that the normal modes localize exponentially according to Anderson theory. In the elastic systems, the localization length decreases with frequency. This behavior is in contrast with what happens in analogous quantum mechanical systems, for which the localization length grows with energy. This difference is explained by means of the properties of the re ection coefficient of a single scatterer in each case.

physics.class-ph↗

arXiv2008

Chaotic scattering with direct processes: A generalization of Poisson's kernel for non-unitary scattering matrices

The problem of chaotic scattering in presence of direct processes or prompt responses is mapped via a transformation to the case of scattering in absence of such processes for non-unitary scattering matrices, \tilde S. In the absence of prompt responses, \tilde S is uniformly distributed according to its invariant measure in the space of \tilde S matrices with zero average, < \tilde S > =0. In the presence of direct processes, the distribution of \tilde S is non-uniform and it is characterized by the average < \tilde S > (\neq 0). In contrast to the case of unitary matrices S, where the invariant measures of S for chaotic scattering with and without direct processes are related through the well known Poisson kernel, here we show that for non-unitary scattering matrices the invariant measures are related by the Poisson kernel squared. Our results are relevant to situations where flux conservation is not satisfied. For example, transport experiments in chaotic systems, where gains or losses are present, like microwave chaotic cavities or graphs, and acoustic or elastic resonators.

cond-mat.mes-hall↗

arXiv2007

Experimental determination of the absorption strength in absorbing chaotic cavities

Due to the experimental necessity we present a formula to determine the absorption strength by power losses inside a chaotic system (cavities, graphs, acoustic resonators, etc) when the antenna coupling, always present in experimental measurements, is taken into account. This is done by calculating the average of the absorption coefficient as a function of the absorption strength and the coupling of the antenna to the system, in the one channel case.

cond-mat.mes-hall↗

arXiv2006

Transport through waveguides with surface disorder

We show that the distribution of the conductance in quasi-one-dimensional systems with surface disorder is correctly described by the Dorokhov-Mello-Pereyra-Kumar equation if one includes direct processes in the scattering matrix S through Poisson's kernel. Although our formulation is valid for any arbitrary number of channels, we present explicit calculations in the one channel case. Ours result is compared with solutions of the Schroedinger equation for waveguides with surface disorder calculated numerically using the R-matrix method.

cond-mat.dis-nn↗

arXiv2006

Wannier-Stark ladders in one-dimensional elastic systems

The optical analogues of Bloch oscillations and their associated Wannier-Stark ladders have been recently analyzed. In this paper we propose an elastic realization of these ladders, employing for this purpose the torsional vibrations of specially designed one-dimensional elastic systems. We have measured, for the first time, the ladder wave amplitudes, which are not directly accessible either in the quantum mechanical or optical cases. The wave amplitudes are spatially localized and coincide rather well with theoretically predicted amplitudes. The rods we analyze can be used to localize different frequencies in different parts of the elastic systems and viceversa.

cond-mat.mes-hall↗

arXiv2005

Interpolation formula for the reflection coefficient distribution of absorbing chaotic cavities in the presence of time reversal symmetry

We propose an interpolation formula for the distribution of the reflection coefficient in the presence of time reversal symmetry for chaotic cavities with absorption. This is done assuming a similar functional form as that when time reversal invariance is absent. The interpolation formula reduces to the analytical expressions for the strong and weak absorption limits. Our proposal is compared to the quite complicated exact result existing in the literature.

cond-mat.mes-hall↗

arXiv2005

Avoided Band Crossing in Locally Periodic Elastic Rods

Avoided band crossings have been studied theoretically and it has been shown that they can provide a tunning of the metal-insulator transition. Here we present an experimental example of an avoided band crossing for a classical undulatory system: torsional waves in locally periodic rods. To excite and detect the torsional waves, an electromagnetic-acoustic transducer for low-frequencies that we have recently developed, is used. Calculations performed using the transfer matrix method agree with the experimental measurements. In the observed avoided band crossing one level, which is a border-induced bulk level, moves from one band to the next.

cond-mat.mes-hall↗

arXiv2004

Distribution of the S-matrix in chaotic microwave cavities with direct processes and 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^{iθ}, 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 based on the Heidelberg approach including absorption. The theoretical result is a generalization of the Poisson kernel. The experimental and the numerical distributions are in excellent agreement with random-matrix predictions for all cases.

cond-mat.mes-hall↗

arXiv2003

Distribution of reflection coefficients in absorbing chaotic microwave cavities

The distributions of the reflection coefficients $P(R)$ for chaotic microwave cavities with time-reversal symmetry are investigated in different absorption and antenna coupling regimes. In all investigated regimes the agreement between the experimental distributions and random matrix result is very good, provided both the antenna coupling $T_a$ and wall absorption strength $T_w$ are properly accounted for. Those parameters are determined by independent experimental quantities.

cond-mat.mes-hall↗

arXiv2003

Fluctuation-Dissipation Theorem for Metastable Systems

We show that an appropriately defined fluctuation-dissipation theorem, connecting generalized susceptibilities and time correlation functions, is valid for times shorter than the nucleation time of the metastable state of Markovian systems satisfying detailed balance. This is done by assuming that such systems can be described by a superposition of the ground and first excited states of the master equation. We corroborate our results numerically for the metastable states of a two-dimensional Ising model.

cond-mat.stat-mech↗

arXiv2000

A Finite Element Algorithm for High-Lying Eigenvalues and Eigenfunctions with Homogeneous Neumann and Dirichlet Boundary Conditions

We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions or combinations of either for different parts of the boundary. In order to solve the generalized eigenvalue problem, we use an inverse power plus Gauss-Seidel algorithm. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We have cheked the algorithm comparing the cumulative level density of the espectrum obtained numerically, with the theoretical prediction given by the Weyl formula. A systematic deviation was found. This deviation is due to the discretisation and not to the algorithm. As an application we calculate the statistical properties of the eigenvalues of the acoustic Bunimovich stadium and compare them with the theoretical results given by random matrix theory.

nlin.CD↗

arXiv1999

Multichannel Quantum Defect Theory: a Quantum Poincare Map

The multichannel quantum defect theory (MQDT) can be reinterpreted as a quantum Poincare map in representation of angular momentum. This has two important implications: we have a paradigm of a true quantum Poincare map without semi-classical input and we get an entirely new insight into the significance of MQDT.

chao-dyn↗

arXiv1999

Vibrating soap films: An analog for quantum chaos on billiards

We present an experimental setup based on the normal modes of vibrating soap films which shows quantum features of integrable and chaotic billiards. In particular, we obtain the so-called scars -narrow linear regions with high probability along classical periodic orbits- for the classically chaotic billiards. We show that these scars are also visible at low frequencies. Finally, we suggest some applications of our experimental setup in other related two-dimensional wave phenomena.

chao-dyn↗

arXiv1999

Structural Invariance and the Energy Spectrum

We extend the application of the concept of structural invariance to bounded time independent systems. This concept, previously introduced by two of us to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the semiclassical limit, is extended to the energy spectra of bounded time independent systems. We proceed by showing that the results obtained previously for the quasi-energies and eigenphases of the S-matrix can be extended to the eigenphases of the quantum Poincare map which is unitary in the semiclassical limit. We then show that its eigenphases in the chaotic case move rather stiffly around the unit circle and thus their local statistical fluctuations transfer to the energy spectrum via Bogomolny's prescription. We verify our results by studying numerically the properties of the eigenphases of the quantum Poincare map for billiards by using the boundary integral method.

chao-dyn↗