Pablo Serra

Comparison study of pivot methods for global optimization

We compare two implementations of a new algorithm called the pivot method for the location of the global minimum of a multiple minima problem. The pivot method uses a series of randomly placed probes in phase space, moving the worst probes to be near better probes iteratively until the system converges. The original implementation, called the “lowest energy pivot method,” chooses the pivot probes with a probability based on the energy of the probe. The second approach, called the “nearest neighbor pivot method,” chooses the pivot probes to be the nearest neighbor points in the phase space. We examine the choice of distribution by comparing the efficiency of the methods for Gaussian versus generalized q-distribution, based on the Tsallis entropy in the relocation of the probes. The two implementations of the method are tested with a series of test functions and with several Lennard-Jones clusters of various sizes. It appears that the nearest neighbor pivot method using the generalized q-distribution is sup...

Quantum critical phenomena and stability of atomic and molecular ions

In this review we discuss quantum phase transitions and the mapping between symmetry breaking of electronic structure configurations at the large-dimension limit and mean-field theory of phase transitions. We show that the finite size scaling method can be used for the calculations of the critical parameters of the few-body Schrodinger equation. In this approach, the finite size corresponds to the number of elements in a complete basis set used to expand the exact eigenfunction of a given Hamiltonian. The critical parameters such as the critical nuclear charges will be used to explain and predict the stability of atomic and molecular negative ions. For N-electron atoms with 2 N 86, results show that, at most, only one electron can be added to a free atom in the gas phase. However, doubly charged atomic negative ions might exist in a strong magnetic field.

Ground-state stability and criticality of two-electron atoms with screened Coulomb potentials using the B-splines basis set

We applied the finite-size scaling method using the B-splines basis set to construct the stability diagram for two-electron atoms with a screened Coulomb potential. The results of this method for two-electron atoms are very accurate in comparison with previous calculations based on Gaussian, Hylleraas and finite-element basis sets. The stability diagram for the screened two-electron atoms shows three distinct regions, i.e. a two-electron region, a one-electron region and a zero-electron region, which correspond to stable, ionized and double ionized atoms, respectively. In previous studies, it was difficult to extend the finite-size scaling calculations to large molecules and extended systems because of the computational cost and the lack of a simple way to increase the number of Gaussian basis elements in a systematic way. Motivated by recent studies showing how one can use B-splines to solve Hartree–Fock and Kohn–Sham equations, this combined finite-size scaling using the B-splines basis set might provide an effective systematic way to treat criticality of large molecules and extended systems. As benchmark calculations, the two-electron systems show the feasibility of this combined approach and provide an accurate reference for comparison. (Some figures may appear in colour only in the online journal)

Excited state entanglement on a two-electron system near the ionization threshold

We have investigated the critical properties of the lowest-energy triplet state of the spherical helium atom. Using finite-size scaling methods we calculate critical charge and critical exponents for both the energy and the von Neumann entropy near the ionization threshold. We show that the scaling properties of the energy and the von Neumann entropy for this excited state are qualitatively different from those obtained for the ground state. These scaling properties are quantified in terms of critical exponents; therefore, the analysis is applicable to other few-fermion systems.

Multicritical phenomena for the hydrogen molecule at the large-dimension limit

Abstract We show that symmetry breaking of the electronic structure configurations for the Hartree-Fock hydrogen molecule at the large-dimension limit can be described as standard phase transitions. The phase diagram in the internuclear distance-nuclear charge plane shows three different stable phases corresponding to different electronic structure configurations. This phase diagram is characterized by a bicritical point where the two continuous phase transition lines join a first order transition line.

Finite size scaling for critical conditions for stable dipole-bound anions

We present a finite-size scaling approach for the calculations of the critical parameters for binding an electron to an electric dipole field. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. The approach is general and could be used to obtain the critical conditions for stable dipole-bound dianions.

CRITICAL PARAMETERS FOR THE HELIUMLIKE ATOMS : A PHENOMENOLOGICAL RENORMALIZATION STUDY

A mapping between the quantum few-body problem and its classical mechanics pseudo-system analog is used to study the critical parameters for the helium isoelectronic sequence. The critical point is the critical value of the nuclear charge Zc for which the energy of a bound state becomes degenerate with a threshold. A finite-size scaling ansatz in the form of a phenomenological renormalization equation is used to obtain very accurate results for the critical point of the ground-state energy, λc=1/Zc=1.0976±0.0004, as well as for the excited 2p2 3P state, λc=1.0058±0.0017. The results for the critical exponents α and ν are also included.

Near-threshold properties of the electronic density of layered quantum dots

Fil: Ferron, Alejandro. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Nordeste. Instituto de Modelado e Innovacion Tecnologica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovacion Tecnologica; Argentina

Finite-size scaling for critical conditions for stable quadrupole-bound anions

We present finite-size scaling calculations of the critical parameters for binding an electron to a finite linear quadrupole field. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. The model Hamiltonian consists of a charge Q located at the origin of the coordinates and k charges -Q/k located at distances R(i), i=1, em leader,k. After proper scaling of distances and energies, the rescaled Hamiltonian depends only on one free parameter q=QR. Two different linear charge configurations with q>0 and q<0 are studied using basis sets in both spherical and prolate spheroidal coordinates. For the case with q>0, the finite size scaling calculations give an extrapolated critical value of q(c)=1.469 70+/-0.000 05 a.u. by using a basis set with prolate spheroidal coordinates. For the quadrupole case with q<0, we obtained an extrapolated critical value of mid R:q(c)mid R:=3.982 51+/-0.000 01 a.u. for stable quadrupole bound anions. The corresponding critical exponent for the ground state energy alpha=1.9964+/-0.0005, with E approximately (q-q(c))(alpha).

Entropy, fidelity, and double orthogonality for resonance states in two-electron quantum dots

Resonance states of a two-electron quantum dots are studied using a variational expansion with both real basis-set functions and complex scaling methods. The two-electron entanglement (linear entropy) is calculated as a function of the electron repulsion at both sides of the critical value, where the ground (bound) state becomes a resonance (unbound) state. The linear entropy and fidelity and double orthogonality functions are compared as methods for the determination of the real part of the energy of a resonance. The complex linear entropy of a resonance state is introduced using complex scaling formalism.