arXiv subjects

E. Hernandez

Publications and source records attributed to E. Hernandez.

72 records · Page 4Linked to original sources

arXiv2002

Jordan blocks and Gamow-Jordan eigenfunctions associated to a double pole of the S-matrix

An accidental degeneracy of resonances gives rise to a double pole in the scattering matrix, a double zero in the Jost function and a Jordan chain of length two of generalized Gamow-Jordan eigenfunctions of the radial Schroedinger equation. The generalized Gamow-Jordan eigenfunctions are basis elements of an expansion in bound and resonant energy eigenfunctions plus a continuum of scattering wave functions of complex wave number. In this biorthonormal basis, any operator which is a regular function of the Hamiltonian is represented by a complex matrix which is diagonal except for a Jordan block of rank two. The occurrence of a double pole in the Green's function, as well as the non-exponential time evolution of the Gamow-Jordan generalized eigenfunctions are associated to the Jordan block in the complex energy representation.

quant-ph↗

arXiv2001

Metric-tensor flexible-cell algorithm for isothermal-isobaric molecular dynamics simulations

An extended Hamiltonian approach to conduct isothermal-isobaric molecular dynamics simulations with full cell flexibility is presented. The components of the metric tensor are used as the fictitious degrees of freedom for the cell, thus avoiding the problem of spurious cell rotations and artificial symmetry breaking effects present in the original Parrinello-Rahman scheme. This is complemented by the Nose-Poincare approach for isothermal sampling. The combination of these two approaches leads to equations of motion that are Hamiltonian in structure, and which can therefore be solved numerically using recently developed powerful symplectic integrators. One such integrator, the generalised leap-frog, is employed to provide a numerical algorithm for integrating the isothermal-isobaric equations of motion obtained.

physics.chem-ph↗

arXiv2000

Modeling the series of (n x 2) Si-rich reconstructions of beta-SiC(001): a prospective atomic wire?

We perform ab initio plane wave supercell density functional calculations on three candidate models of the (3 x 2) reconstruction of the beta-SiC(001) surface. We find that the two-adlayer asymmetric-dimer model (TAADM) is unambiguously favored for all reasonable values of Si chemical potential. We then use structures derived from the TAADM parent to model the silicon lines that are observed when the (3 x 2) reconstruction is annealed (the (n x 2) series of reconstructions), using a tight-binding method. We find that as we increase n, and so separate the lines, a structural transition occurs in which the top addimer of the line flattens. We also find that associated with the separation of the lines is a large decrease in the HOMO-LUMO gap, and that the HOMO state becomes quasi-one-dimensional. These properties are qualititatively and quantitatively different from the electronic properties of the original (3 x 2) reconstruction.

cond-mat.mtrl-sci↗

arXiv2000

Tight Binding Molecular Dynamics Studies of Boron Assisted Nanotube Growth

In this paper we report a theoretical study of the effects of the presence of boron in growing carbon nanotubes. We employ a well established Tight Binding model to describe the interactions responsible for the energetics of these systems, combined with the Molecular Dynamics simulation technique and Structural Relaxation calculations. We find, in agreement with the previous theoretical/experimental work of Blase {\em et al.} [{\em Phys. Rev. Lett.} {\bf 83}, 5078 (1999)], that boron favors (n,0) (zig-zag) tubular structures over (n,n) (arm-chair) ones by stabilizing the zig-zag edge. Furthermore, it is shown that boron has the effect of delaying the tube closure process, a fact which could explain the improved aspect ratio experimentally observed in nanotubes synthesized in the presence of boron. Our dynamical simulations lead us to propose a mechanism through which this extension of the closure time can be explained.

cond-mat.mtrl-sci↗

arXiv1999

van der Waals interaction in nanotube bundles : consequences on vibrational modes

We have developed a pair-potential approach for the evaluation of van der Waals interaction between carbon nanotubes in bundles. Starting from a continuum model, we show that the intertube modes range from $5 cm^{-1}$ to $60 cm^{-1}$. Using a non-orthogonal tight-binding approximation for describing the covalent intra-tube bonding in addition, we confirme a slight chiral dependance of the breathing mode frequency and we found that this breathing mode frequency increase by $\sim$ 10 % if the nanotube lie inside a bundle as compared to the isolated tube.

cond-mat.mtrl-sci↗

arXiv1998

Elastic Properties of Single-Wall Nanotubes

We report results of theoretical studies on the elastic properties of single-wall nanotubes of the following compositions: C, BN, ${BC}_3$, ${BC}_2{N}$ and ${C}_3{N}_4$. These studies have been carried out using a total energy, non-orthogonal tight-binding parametrisation which is shown to provide results in good agreement both with calculations using higher levels of theory and the available experimental data. Our results predict that of all types of nanotubes considered, carbon nanotubes have the highest Young's modulus. We have considered tubes of different diameters, ranging from 0.5 to 2~nm, and find that in the limit of large diameters the mechanical properties of nanotubes approach those of the corresponding flat graphene-like sheets.

cond-mat.mtrl-sci↗

arXiv1998

Two Pion Production in Nucleon-Nucleon Collisions at Intermediate Energies

nucl-th↗

arXiv1998

Isocalar Roper excitation in the pp --> pp pi0 reaction close to threshold

A new mechanism for the pp --> pp pi0 reaction close to threshold is suggested coming from the isoscalar excitation of the Roper and its decay into N(pi pi)S-wave, with one of the pi0 emitted and the other one reabsorbed on the second nucleon. The mechanism can lead to important interference with other mechanisms and, together with experiment, serves to exclude large ranges of the 2pi N* decay parameters allowed by the N* partial decay widths.

nucl-th↗

arXiv1998

Double Pion Production Reactions

We report on reactions producing two pions induced by real and virtual photons or nucleons. The role of different resonances in these reactions is emphasized. Novel results on coherent two pion photoproduction in nuclei are also reported.

nucl-th↗

arXiv1998

Elastic Properties of C and BxCyNz Composite Nanotubes

We present a comparative study of the energetic, structural and elastic properties of carbon and composite single-wall nanotubes, including BN, BC3 and BC2N nanotubes, using a non-orthogonal tight-binding formalism. Our calculations predict that carbon nanotubes have a higher Young modulus than any of the studied composite nanotubes, and of the same order as that found for defect-free graphene sheets. We obtain good agreement with the available experimental results.

cond-mat.mtrl-sci↗

arXiv1998

Theoretical study of the N N --> N N pi pi reaction

We have developed a model for the N N --> N N pi pi reaction and evaluated cross sections for the different charged channels. The low energy part of those channels where the pions can be in an isospin zero state is dominated by N* excitation, driven by an isoscalar source recently found experimentally, followed by the decay N* --> N (pi pi, T=0, s-wave). At higher energies, and in channels where the pions are not in T=0, Delta excitation mechanisms become relevant. A rough agreement with the experimental data is obtained in most channels. Repercussions of the present findings for the ABC effect and the p p --> p p pi0 reaction close to threshold are also suggested.

nucl-th↗

arXiv1997

Accidental Degeneracy and Berry Phase of Resonant States

We study the complex geometric phase acquired by the resonant states of an open quantum system which evolves irreversibly in a slowly time dependent environment. In analogy with the case of bound states, the Berry phase factors of resonant states are holonomy group elements of a complex line bundle with structure group C*. In sharp contrast with bound states, accidental degeneracies of resonances produce a continuous closed line of singularities formally equivalent to a continuous distribution of "magnetic" charge on a "diabolical" circle, in consequence, we find different classes of topologically inequivalent non-trivial closed paths in parameter space.

quant-ph↗

arXiv1996

Electromagnetic Properties of the Delta(1232)

We calculate the electromagnetic moments and radii of the Delta(1232) in the nonrelativistic quark model, including two-body exchange currents. We show that two-body exchange currents lead to nonvanishing Delta and N-->Delta transition quadrupole moments even if the wave functions have no D-state admixture. The usual explanation based on the single-quark transition model involves D-state admixtures but no exchange currents. We derive a parameter- free relation between the N-->Delta transition quadrupole moment and the neutron charge radius: Q(N-->Delta) = r^2(neutron)/sqrt(2). Furthermore, we calculate the M1 and E2 amplitudes for the process photon + N -->Delta. We find that the E2 amplitude receives sizeable contributions from exchange currents. These are more important than the ones which result from D-state admixtures due to tensor forces between quarks if a reasonable quark core radius of about 0.6 fm is used. We obtain a ratio of E2/M1=-3.5%.

nucl-th↗

arXiv1996

Basis Functions for Linear-Scaling First-Principles Calculations

In the framework of a recently reported linear-scaling method for density-functional-pseudopotential calculations, we investigate the use of localized basis functions for such work. We propose a basis set in which each local orbital is represented in terms of an array of `blip functions'' on the points of a grid. We analyze the relation between blip-function basis sets and the plane-wave basis used in standard pseudopotential methods, derive criteria for the approximate equivalence of the two, and describe practical tests of these criteria. Techniques are presented for using blip-function basis sets in linear-scaling calculations, and numerical tests of these techniques are reported for Si crystal using both local and non-local pseudopotentials. We find rapid convergence of the total energy to the values given by standard plane-wave calculations as the radius of the linear-scaling localized orbitals is increased.

mtrl-th↗

arXiv1996

Berry Phase of a Resonant State

We derive closed analytical expressions for the complex Berry phase of an open quantum system in a state which is a superposition of resonant states and evolves irreversibly due to the spontaneous decay of the metastable states. The codimension of an accidental degeneracy of resonances and the geometry of the energy hypersurfaces close to a crossing of resonances differ significantly from those of bound states. We discuss some of the consequences of these differences for the geometric phase factors, such as: Instead of a diabolical point singularity there is a continuous closed line of singularities formally equivalent to a continuous distribution of `magnetic' charge on a diabolical circle; different classes of topologically inequivalent non-trivial closed paths in parameter space, the topological invariant associated to the sum of the geometric phases, dilations of the wave function due to the imaginary part of the Berry phase and others.

hep-th↗

arXiv1995

Towards a Linear-Scaling DFT Technique: The Density Matrix Approach

A recently proposed linear-scaling scheme for density-functional pseudopotential calculations is described in detail. The method is based on a formulation of density functional theory in which the ground state energy is determined by minimization with respect to the density matrix, subject to the condition that the eigenvalues of the latter lie in the range [0,1]. Linear-scaling behavior is achieved by requiring that the density matrix should vanish when the separation of its arguments exceeds a chosen cutoff. The limitation on the eigenvalue range is imposed by the method of Li, Nunes and Vanderbilt. The scheme is implemented by calculating all terms in the energy on a uniform real-space grid, and minimization is performed using the conjugate-gradient method. Tests on a 512-atom Si system show that the total energy converges rapidly as the range of the density matrix is increased. A discussion of the relation between the present method and other linear-scaling methods is given, and some problems that still require solution are indicated.

mtrl-th↗

arXiv1995

Off shell pi N amplitude and the p p->p p pi0 reaction

We have used a conventional model for the $pp \rightarrow pp π^{0}$ reaction consisting of the Born term plus the $s$-wave rescattering term. As a novelty we have introduced the off shell dependence of the $πN$ $s$-wave isoscalar amplitude. This amplitude is appreciably enhanced when one moves to the off shell situations met in the problem and, as a consequence, the $pp \rightarrow pp π^{0}$ cross section becomes considerably larger than with the use of the $πN$ on shell amplitudes. Two different models for the off shell extrapolation found in the literature have been used and the cross sections obtained are large enough to account for the experimental data, although uncertainties remain due to the incomplete knowledge of the off shell extrapolation.

nucl-th↗

arXiv1995

A Self-Consistent First-Principles Technique Having Linear Scaling

An algorithm for first-principles electronic structure calculations having a computational cost which scales linearly with the system size is presented. Our method exploits the real-space localization of the density matrix, and in this respect it is related to the technique of Li, Nunes and Vanderbilt. The density matrix is expressed in terms of localized support functions, and a matrix of variational parameters, L, having a finite spatial range. The total energy is minimized with respect to both the support functions and the elements of the L matrix. The method is variational, and becomes exact as the ranges of the support functions and the L matrix are increased. We have tested the method on crystalline silicon systems containing up to 216 atoms, and we discuss some of these results.

mtrl-th↗