arXiv subjects

Pedro Contreras

Publications and source records attributed to Pedro Contreras.

16 recordsLinked to original sources

arXiv2023

Self-Consistent Study of the Superconducting Gap in the Strontium-doped Lanthanum Cuprate

This work is aimed at numerically investigating the behavior of the Fermi energy in Strontium-doped Lanthanum Cuprate, using a numerical zero temperature elastic scattering cross-section procedure in the unitary collision regime. The main task is to vary the zero temperature superconducting energy gap from its zero value in the normal state, to the highest value of 60 meV. We find that there are two different reduced phase space regimes for the first harmonic line node's order parameter. The first scenario considers that when the Fermi energy and the nearest hopping terms have the same order of magnitude, the physics can be described by a picture given by nonequilibrium statistical mechanics. A second scenario indicates, that when the Fermi energy parameter and the hopping term have different order of magnitude; the physical picture tends to be related to the nonrelativistic quantum mechanical degrees of freedom coming from quasi-stationary quantum energy levels, with a damping term seen in the probability density distribution function, that is described in the configuration space. Henceforth, it is concluded that the use of the zero temperature elastic scattering cross-section links the phase and configuration spaces through the inverse scattering lifetime, and helps to clarify the role of the degrees of freedom in Strontium-doped Lanthanum Cuprate. Finally, we think that the self-consistent numerical procedure with the reduced phase space, induces nonlocality in the inverse scattering lifetime.

cond-mat.supr-con↗

arXiv2023

The collision frequency in two unconventional superconductors

The collision frequency (also known as the inverse scattering lifetime) can be self-consistently calculated from the imaginary part of the zero-temperature elastic scattering cross-section in unconventional superconductors. We find these types of studies helpful to describe a hidden self-consistent damping due to incoherent fermions in two physical spaces: The Phase Space of the Nonequilibrium Statistical Mechanics, and the Configuration Space of Nonrelativistic Quantum Mechanics. The direct relation of the collision frequency with those well-known Physical Spaces is addressed in a singular way this time. Since the use of collisions for different elastic scattering regimes, is a well-developed formalism using retarded, and advanced Green functions in Many Body Physics; in order to describe our findings, we define and characterize a Reduced Phase Space for collision frequencies in the triplet strontium ruthenate compound and the singlet doped with strontium lanthanum cuprate ceramic. Both compounds display different nodal behavior of the superconducting order parameter. In this work, their zero gap behavior is numerically scanned and used to give some illustrative examples. Finally, it intuitively explores the geometrical nonlocality of the collision frequency of this type of hidden self-consistency in the Boltzmann equation, when the zero superconducting gap value drives the physics below the transition temperature, and incoherent fermions quasiparticles govern several nonequilibrium phenomena since the macroscopic behavior remarkably changes with the strontium atomic potential strength, and the concentration inherent to both compounds.

cond-mat.supr-con↗

arXiv2022

Tight-Binding Superconducting Phases in the Unconventional Compounds Strontium-Substituted Lanthanum Cuprate and Strontium Ruthenate

We use the idea of the Wigner probability distribution (WPD) in a reduced scattering phase space (RPS) for the elastic scattering cross-section, with the help of a Tight-Binding (TB) numerical procedure allowing us to consider the anisotropic quantum effects, to phenomenologically predict several phases in these two novel unconventional superconductors. Unlike our previous works with pieces of evidence that these two compounds are in the unitary strong scattering regime and that superconductivity is suppressed by the atoms of strontium in both materials, several phases are built. In the case of the strontium-substituted lanthanum cuprate, it was found three phases from one family of Wigner probabilistic distributions, one corresponding to the antiferromagnetic compound La2CuO4 another one which consists of a coalescing metallic phase for very lightly doped La2-xSrxCuO4, and finally a strong self-consistent dependent strange metal phase with optimal levels of doping. In the case of a triplet superconductor strontium ruthenate, three phases can be differentiated from two families of Wigner distribution probabilities, one family of WDP with point nodes where Cooper pairs and dressed scattered normal quasiparticles are mixed for the whole range of frequencies and which correspond to an FS $\gamma$ flat-sheet in the ground metallic state, and two phases from another WPD family, where, in one of then, the Miyake-Narikiyo quasinodal tiny gap model allows the unique presence of Cooper pairs in a tiny interval of frequencies near the superconducting transition TC, the other phase corresponds to the mixed-phase with Cooper pairs and dressed by stoichiometric strontium non-magnetic atoms, where strong self-consistent effects are noticeable. This approach allows comparing experimental results for samples in both compounds with numerical analysis studies.

cond-mat.supr-con↗

arXiv2019

Inversion of walkaway VSP data in the presence of lateral velocity heterogeneity

Multi-azimuth walkaway vertical seismic profiling (VSP) is an established technique for the estimation of in situ slowness surfaces and inferring anisotropy parameters. Normally, this the technique requires the assumption of lateral homogeneity, which makes the horizontal slowness components at depths of downhole receivers equal to those measured at the surface. Any violations of this assumption, such as lateral heterogeneity or a nonzero dip of intermediate interfaces, lead to distortions in reconstructed slowness surfaces and, consequently, to errors in estimated anisotropic parameters. Here, we relax the assumption of lateral homogeneity and discuss how to correct VSP data for weak, lateral heterogeneity (LH). We describe a procedure of downward continuation of recorded travel times that accounts for the presence of both vertical inhomogeneity and weak lateral heterogeneity, which produces correct slowness surfaces at depths of downhole receivers. Once the slowness surfaces are found and the desired type of anisotropic model to be inverted is selected, the corresponding anisotropic parameters, providing the best fit to the estimated slowness can be obtained. We invert the slowness surfaces of $P$-waves for parameters of the simplest anisotropic model describing dipping fractures -- transversely isotropic medium with a tilted symmetry axis. Five parameters of this model -- the $P$-wave velocity $V_0$ in the direction of the symmetry axis, Thomsen's anisotropic coefficients $\epsilon$ and $\delta$, the tilt $\nu$, and the azimuth $\beta$ of the symmetry axis can be estimated in a stable manner when maximum source offset is greater than half of the receiver depth.

physics.geo-ph↗

arXiv2018

A numerical calculation of the electronic specific heat for the compound Sr$_2$RuO$_4$ below its superconducting transition temperature

In this work, a numerical study of the superconducting specific heat of the unconventional multiband superconductor Strontium Ruthenate is performed. Two band gaps models are employed, and the results rendered for each of them are compared. One of the models, previously proposed by one of the authors to explain the experimental temperature behavior of the ultrasound attenuation, considers two gaps with point nodes of different magnitude on different gap surface sheets, while the other one is an isotropic and line node model, reported in the literature for describing quantitatively experimental specific heat data. The superconducting density of states DOS is computed by employing these two models and then, a detailed numerical study of the electronic specific heat, that includes the contribution from the different Fermi sheets, is carried out. It is found that the calculated point node model specific heat temperature behavior shows an excellent agreement with the existent Sr$_2$RuO$_4$ experimental data at zero field, particularly, it is obtained that the observed specific heat jump at T$_c$ is precisely reproduced. Also, it is found that the sum of the contributions from the different bands fits quantitatively the measured specific heat data. The results in this work evidence that the Sr$_2$RuO$_4$ superconducting states are of unconventional nature, corresponding to those of a point node superconductor, and show the importance of taking into account the multiband nature of the material when calculating thermodynamic superconducting quantities.

cond-mat.supr-con↗

arXiv2018

Symmetry Field Breaking Effects in Sr$_2$RuO$_4$

In this work, after reviewing the theory of the elastic properties of Strontium ruthenate, an extension suitable to explain the sound speed experiments of Lupien et. al. \protect\cite{lup2} and Clifford et. al. \protect\cite{clif1} is carried out. It is found that the discontinuity in the elastic constant C$_{66}$ gives unambiguous experimental evidence that the \sr superconducting order parameter $Ψ$ has two components and shows a broken time-reversal symmetry state. A detailed study of the elastic behavior is performed by means of a phenomenological theory employing the Ginzburg-Landau formalism.

cond-mat.supr-con↗

arXiv2018

Ellipsoidal impulse responses in fractured media

Multiple vertical fracture sets, combined with horizontal fine layering produce an equivalent medium of orthorhombic or monoclinic symmetry. This is particularly important in fracture reservoir characterization. Fractured reservoirs are azimuthal anisotropic with respect to elastic-wave propagation. In this work we introduce an ellipsoidal approximation for monoclinic media that is able to characterized fractured media near the vertical axis of symmetry. The procedure is basically two-fold. First, we estimate phase velocities near the vertical axis using an expansion of the slowness. Secondly, the phase velocities are used to build the group velocities near the vertical axis. We particularly establish that for monoclinic media ellipsoidal functions in the phase domain correspond to ellipsoidal functions in the group domain. Finally, in order to validate the approximation, the $P$, $S_1$ and $S_2$ ellipsoidal impulse responses are compared for different polar angles with the exact responses obtained by solving numerically the eigenvectors problem from the Christoffel equation. Examples are shown for monoclinic media, and are validated showing results from a previous work for orthorhombic media. The whole procedure is valid for homogeneous media.

physics.geo-ph↗

arXiv2018

On the geometric and magnetic properties of the monomer, dimer and trimer of NiFe2O4

In this work, by employing Density Functional Theory, we compute and discuss some geometric and magnetic properties of the monomer, dimer and trimer of NiFe2 O4 . The calculations are performed at the UDFT/ B3LYP level of calculation, by employing the LANL2DZ effective pseudo potential. The results of the Mulliken spin densities and the spin polarization will be presented. Finally the outcome of the system density of states is considered.

cond-mat.mtrl-sci↗

arXiv2012

The Future of Search and Discovery in Big Data Analytics: Ultrametric Information Spaces

Consider observation data, comprised of n observation vectors with values on a set of attributes. This gives us n points in attribute space. Having data structured as a tree, implied by having our observations embedded in an ultrametric topology, offers great advantage for proximity searching. If we have preprocessed data through such an embedding, then an observation's nearest neighbor is found in constant computational time, i.e. O(1) time. A further powerful approach is discussed in this work: the inducing of a hierarchy, and hence a tree, in linear computational time, i.e. O(n) time for n observations. It is with such a basis for proximity search and best match that we can address the burgeoning problems of processing very large, and possibly also very high dimensional, data sets.

cs.IR↗

arXiv2011

Fast, Linear Time, m-Adic Hierarchical Clustering for Search and Retrieval using the Baire Metric, with linkages to Generalized Ultrametrics, Hashing, Formal Concept Analysis, and Precision of Data Measurement

We describe many vantage points on the Baire metric and its use in clustering data, or its use in preprocessing and structuring data in order to support search and retrieval operations. In some cases, we proceed directly to clusters and do not directly determine the distances. We show how a hierarchical clustering can be read directly from one pass through the data. We offer insights also on practical implications of precision of data measurement. As a mechanism for treating multidimensional data, including very high dimensional data, we use random projections.

stat.ML↗

arXiv2011

Fast, Linear Time Hierarchical Clustering using the Baire Metric

The Baire metric induces an ultrametric on a dataset and is of linear computational complexity, contrasted with the standard quadratic time agglomerative hierarchical clustering algorithm. In this work we evaluate empirically this new approach to hierarchical clustering. We compare hierarchical clustering based on the Baire metric with (i) agglomerative hierarchical clustering, in terms of algorithm properties; (ii) generalized ultrametrics, in terms of definition; and (iii) fast clustering through k-means partititioning, in terms of quality of results. For the latter, we carry out an in depth astronomical study. We apply the Baire distance to spectrometric and photometric redshifts from the Sloan Digital Sky Survey using, in this work, about half a million astronomical objects. We want to know how well the (more costly to determine) spectrometric redshifts can predict the (more easily obtained) photometric redshifts, i.e. we seek to regress the spectrometric on the photometric redshifts, and we use clusterwise regression for this.

stat.ML↗

arXiv2011

Methods of Hierarchical Clustering

We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps, and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally we describe a recently developed very efficient (linear time) hierarchical clustering algorithm, which can also be viewed as a hierarchical grid-based algorithm.

cs.IR↗

arXiv2011

Fast redshift clustering with the Baire (ultra) metric

The Baire metric induces an ultrametric on a dataset and is of linear computational complexity, contrasted with the standard quadratic time agglomerative hierarchical clustering algorithm. We apply the Baire distance to spectrometric and photometric redshifts from the Sloan Digital Sky Survey using, in this work, about half a million astronomical objects. We want to know how well the (more cos\ tly to determine) spectrometric redshifts can predict the (more easily obtained) photometric redshifts, i.e. we seek to regress the spectrometric on the photometric redshifts, and we develop a clusterwise nearest neighbor regression procedure for this.

cs.IR↗

arXiv2010

Hierarchical Clustering for Finding Symmetries and Other Patterns in Massive, High Dimensional Datasets

Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. "Structure" can be understood as symmetry and a range of symmetries are expressed by hierarchy. Such symmetries directly point to invariants, that pinpoint intrinsic properties of the data and of the background empirical domain of interest. We review many aspects of hierarchy here, including ultrametric topology, generalized ultrametric, linkages with lattices and other discrete algebraic structures and with p-adic number representations. By focusing on symmetries in data we have a powerful means of structuring and analyzing massive, high dimensional data stores. We illustrate the powerfulness of hierarchical clustering in case studies in chemistry and finance, and we provide pointers to other published case studies.

stat.ML↗

arXiv2009

Scale-Based Gaussian Coverings: Combining Intra and Inter Mixture Models in Image Segmentation

By a "covering" we mean a Gaussian mixture model fit to observed data. Approximations of the Bayes factor can be availed of to judge model fit to the data within a given Gaussian mixture model. Between families of Gaussian mixture models, we propose the Rényi quadratic entropy as an excellent and tractable model comparison framework. We exemplify this using the segmentation of an MRI image volume, based (1) on a direct Gaussian mixture model applied to the marginal distribution function, and (2) Gaussian model fit through k-means applied to the 4D multivalued image volume furnished by the wavelet transform. Visual preference for one model over another is not immediate. The Rényi quadratic entropy allows us to show clearly that one of these modelings is superior to the other.

cs.CV↗

arXiv2004

Determining the superconducting gap structure in Sr2RuO4 from sound attenuation studies below Tc

This work presents a quantitative theoretical study of the sound attenuation in the unconventional multiband superconductor Sr2RuO4 below the superconducting transition temperature Tc. Sound attenuation in this material is shown to have the remarkable property of being able to identify different nodal structures on different bands. The nodal structures on the γband on the one hand, and on the αand βbands on the other, are both found to be characterized by the existence of point nodes, but are significantly different in their quantitative aspects.

cond-mat.supr-con↗