Effective t-J model Hamiltonian parameters of monolayered cuprate superconductors from ab initio electronic structure calculations

The magnetic coupling constant of selected cuprate superconductor parent compounds has been determined by means of embedded cluster model and periodic calculations carried out at the same level of theory. The agreement between both approaches validates the cluster model. This model is subsequently employed in state-of-the-art configuration interaction calculations aimed to obtain accurate values of the magnetic coupling constant and hopping integral for a series of superconducting cuprates. Likewise, a systematic study of the performance of different ab initio explicitly correlated wave function methods and of several density functional approaches is presented. The accurate determination of the parameters of the t-J Hamiltonian has several consequences. First, it suggests that the appearance of high-Tc superconductivity in existing monolayered cuprates occurs with J/t in the 0.20¿0.35 regime. Second, J/t=0.20 is predicted to be the threshold for the existence of superconductivity and, third, a simple and accurate relationship between the critical temperatures at optimum doping and these parameters is found. However, this quantitative electronic structure versus Tc relationship is only found when both J and t are obtained at the most accurate level of theory.

Semiclassical evaluation of average nuclear one- and two-body matrix elements

Thomas-Fermi theory is developed to evaluate nuclear matrix elements averaged on the energy shell, on the basis of independent particle Hamiltonians. One- and two-body matrix elements are compared with the quantal results, and it is demonstrated that the semiclassical matrix elements, as function of energy, well pass through the average of the scattered quantum values. For the one-body matrix elements it is shown how the Thomas-Fermi approach can be projected on good parity and also on good angular momentum. For the two-body case, the pairing matrix elements are considered explicitly.

A chemical Hamiltonian approach study of the basis set superposition error changes on electron densities and one- and two-center energy components

A comparision of the local effects of the basis set superposition error (BSSE) on the electron densities and energy components of three representative H-bonded complexes was carried out. The electron densities were obtained with Hartee-Fock and density functional theory versions of the chemical Hamiltonian approach (CHA) methodology. It was shown that the effects of the BSSE were common for all complexes studied. The electron density difference maps and the chemical energy component analysis (CECA) analysis confirmed that the local effects of the BSSE were different when diffuse functions were present in the calculations

Effect of basis set superposition error on the electron density of molecular complexes

The effect of basis set superposition error (BSSE) on molecular complexes is analyzed. The BSSE causes artificial delocalizations which modify the first order electron density. The mechanism of this effect is assessed for the hydrogen fluoride dimer with several basis sets. The BSSE-corrected first-order electron density is obtained using the chemical Hamiltonian approach versions of the Roothaan and Kohn-Sham equations. The corrected densities are compared to uncorrected densities based on the charge density critical points. Contour difference maps between BSSE-corrected and uncorrected densities on the molecular plane are also plotted to gain insight into the effects of BSSE correction on the electron density

Second-order Møller-Plesset perturbation theory without basis set superposition error : II : open-shell systems

The basis set superposition error-free second-order MØller-Plesset perturbation theory of intermolecular interactions was studied. The difficulties of the counterpoise (CP) correction in open-shell systems were also discussed. The calculations were performed by a program which was used for testing the new variants of the theory. It was shown that the CP correction for the diabatic surfaces should be preferred to the adiabatic ones

Charge transfer in DNA: hole charge is confined to a single base pair due to solvation effects

We include solvation effects in tight-binding Hamiltonians for hole states in DNA. The corresponding linear-response parameters are derived from accurate estimates of solvation energy calculated for several hole charge distributions in DNA stacks. Two models are considered: (A) the correction to a diagonal Hamiltonian matrix element depends only on the charge localized on the corresponding site and (B) in addition to this term, the reaction field due to adjacent base pairs is accounted for. We show that both schemes give very similar results. The effects of the polar medium on the hole distribution in DNA are studied. We conclude that the effects of polar surroundings essentially suppress charge delocalization in DNA, and hole states in (GC)n sequences are localized on individual guanines

C---H local modes in cyclobutene, part I: FTIR studies, 600 to 10000 cm–1

The vibrational structure of C---H stretching states in gas-phase cyclobutene was studied using FTIR spectroscopy in the range 700–9000 cm−1. The structure was modelled using two effective vibrational Hamiltonians, one for each type of C---H bond present, consisting of local mode basis functions subject to coupling with symmetrically equivalent bonds and to Fermi resonances with suitable low frequency vibrations. Best-fit model parameters were determined using least-squares routines and the model predictions are compared to the observed band positions and intensities. Some discussion is given of the relevance of the observed couplings to intramolecular vibrational redistribution (IVR) which results in the observation of statistical behaviour in cyclobutene isomerization induced by excitation of C---H stretching overtones in the visible region.

Self-adjoint extensions and spectral analysis in the Calogero problem

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential alpha x(-2). Although the problem is quite old and well studied, we believe that our consideration based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in our previous works, adds some new points to its solution. To demonstrate that a consideration of the Calogero problem requires mathematical accuracy, we discuss some `paradoxes` inherent in the `naive` quantum-mechanical treatment. Using a self-adjoint extension method, we construct and study all possible self-adjoint operators (self-adjoint Hamiltonians) associated with a formal differential expression for the Calogero Hamiltonian. In particular, we discuss a spontaneous scale-symmetry breaking associated with self-adjoint extensions. A complete spectral analysis of all self-adjoint Hamiltonians is presented.

A general treatment of geometric phases and dynamical invariants

Based only on the parallel-transport condition, we present a general method to compute Abelian or non-Abelian geometric phases acquired by the basis states of pure or mixed density operators, which also holds for nonadiabatic and noncyclic evolution. Two interesting features of the non-Abelian geometric phase obtained by our method stand out: i) it is a generalization of Wilczek and Zee`s non-Abelian holonomy, in that it describes nonadiabatic evolution where the basis states are parallelly transported between distinct degenerate subspaces, and ii) the non-Abelian character of our geometric phase relies on the transitional evolution of the basis states, even in the nondegenerate case. We apply our formalism to a two-level system evolving nonadiabatically under spontaneous decay to emphasize the non- Abelian nature of the geometric phase induced by the reservoir. We also show, through the generalized invariant theory, that our general approach encompasses previous results in the literature. Copyright (c) EPLA, 2008.

A influência do esqueleto açúcar-fostato no transporte da molécula de DNA

This dissertation analyses the influence of sugar-phosphate structure in the electronic transport in the double stretch DNA molecule, with the sequence of the base pairs modeled by two types of quasi-periodic sequences: Rudin-Shapiro and Fibonacci. For the sequences, the density of state was calculated and it was compared with the density of state of a piece of human DNA Ch22. After, the electronic transmittance was investigated. In both situations, the Hamiltonians are different. On the analysis of density of state, it was employed the Dyson equation. On the transmittance, the time independent Schrödinger equation was used. In both cases, the tight-binding model was applied. The density of states obtained through Rudin-Shapiro sequence reveal to be similar to the density of state for the Ch22. And for transmittance only until the fifth generation of the Fibonacci sequence was acquired. We have considered long range correlations in both transport mechanism

Variational supersymmetric approach to evaluate Fokker-Planck probability

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Deformations of N=2 superconformal algebra and supersymmetric two-component Camassa-Holm equation

This paper is concerned with a link between central extensions of N = 2 superconformal algebra and a supersymmetric two-component generalization of the Camassa-Holm equation. Deformations of superconformal algebra give rise to two compatible bracket structures. One of the bracket structures is derived from the central extension and admits a momentum operator which agrees with the Sobolev norm of a co-adjoint orbit element. The momentum operator induces, via Lenard relations, a chain of conserved Hamiltonians of the resulting supersymmetric Camassa-Holm hierarchy.

On negative flows of the AKNS hierarchy and a class of deformations of a bihamiltonian structure of hydrodynamic type

A deformation parameter of a bihamiltonian structure of hydrodynamic type is shown to parametrize different extensions of the AKNS hierarchy to include negative flows. This construction establishes a purely algebraic link between, on the one hand, two realizations of the first negative flow of the AKNS model and, on the other, two-component generalizations of Camassa-Holmand Dym-type equations. The two-component generalizations of Camassa-Holm- and Dym-type equations can be obtained from the negative-order Hamiltonians constructed from the Lenard relations recursively applied on the Casimir of the first Poisson bracket of hydrodynamic type. The positive-order Hamiltonians, which follow froth the Lenard scheme applied on the Casimir of the second Poisson bracket of hydrodynamic type, are shown to coincide with the Hamiltonians of the AKNS model. The AKNS Hamiltonians give rise to charges conserved with respect to equations of motion of two-component Camassa-Holm- and two-component Dym-type equations.

Renormalization in few-body nuclear physics

Renormalized fixed-point Hamiltonians are formulated for systems described by interactions that originally contain point-like singularities (as the Dirac-delta and/or its derivatives). They express the renormalization group invariance of quantum mechanics. The present approach for the renormalization scheme relies on a subtracted T-matrix equation.

Many-body theory for systems of composite hadrons

Many-body systems of composite hadrons are characterized by processes that involve the simultaneous presence of hadrons and their constituents. We briefly review several methods that have been devised to study such systems and present a novel method that is based on the ideas of mapping between physical and ideal Fock spaces. The method, known as the Fock-Tani representation, was invented years ago in the context of atomic physics problems and was recently extended to hadronic physics. Starting with the Fock-space representation of single-hadron states, a change of representation is implemented by a unitary transformation such that composites are redescribed by elementary Bose and Fermi field operators in an extended Fock space. When the unitary transformation is applied to the microscopic quark Hamiltonian, effective, Hermitian Hamiltonians with a clear physical interpretation are obtained. The use of the method in connection with the linked-cluster formalism to describe short-range correlations and quark deconfinement effects in nuclear matter is discussed. As an application of the method, an effective nucleon-nucleon interaction is derived from a constituent quark model and used to obtain the equation of state of nuclear matter in the Hartree-Fock approximation.