arXiv subjects

V. Domínguez-Rocha

Publications and source records attributed to V. Domínguez-Rocha.

7 recordsLinked to original sources

arXiv2026

Exceptional Points revealed by the integrated imaginary scattering eigenphase

We propose and analytically demonstrate that the eigenphases of the scattering matrix provide direct, phase-sensitive signatures of exceptional points in open PT-symmetric systems. Using a one-dimensional PT-symmetric quantum dimer with balanced gain and loss, coupled to continuum leads, we track the evolution of the scattering eigenphases across the PT-exact to PT-broken transition. The imaginary parts of the eigenphases develop localized structures of opposite sign as the exceptional point is approached, reflecting the emergence of gain/loss asymmetry in the scattering eigenmodes. We introduce the integrated imaginary scattering eigenphase G(gamma), which condenses this information into a single experimentally accessible scalar. G(gamma) is negligibly small in the PT-exact phase and undergoes a sharp transition -- a pronounced inflection followed by saturation into a plateau -- near the exceptional point. The inflection point of G(gamma) precedes gamma_{EP} and coincides with the maximum amplitude of the transmission resonances, revealing that peak gain/loss asymmetry and eigenstate coalescence are governed by independent conditions in open systems -- a direct fingerprint of their finite coupling to the continuum. Because the analysis is formulated entirely at the level of the S-matrix -- without reference to any specific physical realization -- the results are universally applicable across wave systems, including photonic, acoustic, and microwave platforms where phase-resolved measurements are available.

quant-ph↗

arXiv2023

The rise and fall of the amplitude, and phase, around Exceptional Points: a Scattering matrix approach

We analyze the behavior of a non-Hermitian opened one-dimensional quantum system with $\mathcal{PT}$ symmetry. This system is built by a dimer, with balanced gains and losses described by a parameter $\gamma$. By varying $\gamma$ the system resonances, which are naturally separated, coalesce at the exceptional point (EP). The transmission spectrum is obtained by means of the scattering matrix ($S$ matrix) formalism and we examine the wave functions corresponding to the resonances as a function of $\gamma$. Specifically, we look for the behavior and distribution of the phases of the $S$ matrix before, at and after the EP.

quant-ph↗

arXiv2020

Sound field radiated by a rod

We study the acoustical intensity field radiated by a thin cylindrical rod vibrating in its lowest compressional mode. Due to the cylindrical symmetry, the emitted field is measured in a radial plane of the rod which is sufficient to reconstruct the full three-dimensional field. Starting from the one-dimensional approximation of the excited compressional mode, we develop a simplified theoretical wave equation which allows for a semi-analytical solution for the emitted wave field. The agreement between the experimental results and the semi-analytical solution is eloquent.

physics.app-ph↗

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↗

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↗

arXiv2014

Planck Scale Induced Speed of Sound in a Trapped Bose-Einstein Condensate

In the present work, we analyze the corrections caused by an anomalous dispersion relation, suggested in several quantum gravity models, upon the speed of sound in a weakly interacting Bose--Einstein Condensate, trapped in a potential of the form $V(r)\sim r^{2}$. We show that the corresponding ground state energy and consequently, the associated speed of sound, present corrections respect to the usual case, which may be used to explore the sensitivity to Planck--scale effects on these relevant properties associated with the condensate. Indeed, we stress that this type of macroscopic bodies may be more sensitive, under certain conditions, to Planck--scale manifestations than its constituents. In addition, we prove that the inclusion of a trapping potential, together with many--body contributions, improves the sensitivity to Planck--scale signals, compared to the homogeneous system.

gr-qc↗