A study of two-electron quantum dot spectrum using discrete variable representation method

A variational method called discrete variable representation is applied to study the energy spectra of two interacting electrons in a quantum dot with a three-dimensional anisotropic harmonic confinement potential. This method, applied originally to problems in molecular physics and theoretical chemistry, is here used to solve the eigenvalue equation to relative motion between the electrons. The two-electron quantum dot spectrum is determined then with a precision of at least six digits. Moreover, the electron correlation energies for various potential confinement parameters are investigated for singlet and triplet states. When possible, the present results are compared with the available theoretical values.     

Functional analysis concepts and Hartree-Fock instability conditions II: An analysis of the eight classes of solutions

The continuation of the previous work is presented. Here the instability matrices for the eight classes of HF solutions, considering time reversal and spin symmetries, are derived and explicitly shown. These matrices are expressed in terms of LCAO coefficients. Hence they are of immediate application to the verification of instabilities in HF calculations.     

Galilean-Covariant Clifford Algebras in the Phase-Space Representation

We apply the Galilean covariant formulation of quantum dynamics to derive the phase-space representation of the Pauli–Schrödinger equation for the density matrix of spin-1/2 particles in the presence of an electromagnetic field. The Liouville operator for the particle with spin follows from using the Wigner–Moyal transformation and a suitable Clifford algebra constructed on the phase space of a (4 + 1)-dimensional space–time with Galilean geometry. Connections with the algebraic formalism of thermofield dynamics are also investigated.     

Partitioning technique procedure revisited: Formalism and first application to atomic problems

Usually the partitioning technique (PT) has been studied under two aspects: (i) as a numerical tool for solving secular equations of high order, and (ii) as a theoretical method related to the infinite‐order perturbation theory and the iteration–variation methods. Here it is shown that there exists a form of the PT equations which allows us to determine explicitly the spectrum and eigenstates of the Hamiltonian operator for different forms of potentials without the utilization of perturbative expansions or iterative equations of the type E=f(E). As a first application of the new approach, we consider the hydrogen‐atom in strong magnetic fields (B ~ 10⁹ G). This revised version was published online in July 2006 with corrections to the Cover Date.     

An Approach by Representation of Algebras for Decoherence-Free Subspaces

The aim of this paper is to present a general algebraic formulation for the decoherence-free subspaces (DFSs). In order to build the DFSs we consider the tensor product of Clifford algebras and left minimal ideals. States, error operators and projection operators are defined in a purely algebraic point of view. For this purpose, we initially generalize some results of Pauli and Artin about semisimple algebras. Then we derive orthogonality theorems for associative algebras analogous to theorems for finite groups. Some advantages and perspectives are also discussed.     

Controls over spatial and seasonal variations on isotopic composition of the precipitation along the central and eastern portion of Brazil

Based on Global Network Isotopes in Precipitation (GNIP) isotopic data set, a review of the spatial and temporal variability of δ¹⁸O and δ²H in precipitation was conducted throughout central and eastern Brazil, indicating that dynamic interactions between Intertropical and South Atlantic Convergence Zones, Amazon rainforest, and Atlantic Ocean determine the variations on the isotopic composition of precipitation over this area. Despite the seasonality and latitude effects observed, a fair correlation with precipitation amount was found. In addition, Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) air mass back trajectories were used to quantify the factors controlling daily variability in stable isotopes in precipitation. Through a linear multiple regression analysis, it was observed that temporal variations were consistent with the meteorological parameters derived from HYSPLIT, particularly precipitation amount along the trajectory and mix depth, but are not dependent on vapour residence time in the atmosphere. These findings also indicate the importance of convective systems to control the isotopic composition of precipitation in tropical and subtropical regions.     

Perturbative symplectic field theory and Wigner function

We study relativistic quantum field theories in phase space, based on representations of the Poincaré group, using the Moyal product. We develop a perturbative theory for quantizing fields, with functional methods in phase space. The two-point function is related to relativistic Wigner functions for bosons and fermions. As an example we analyze the complex scalar field with quartic self-interaction.     

Functional analysis concepts and Fartree-Fock instability conditions

Concepts of functional analysis, namely, regular points, tangent subspaces, constraint surfaces, Lagrangian matrix restricted to the tangent subspace of a constraint surface, are presented in connection with the Hartree-Fock (HF) problem. The energy functional in LCAO approximation is considered to be a polynomial function of several variables subject to subsidiary conditions. General HF equations and instability conditions for the unrestricted Hartree-Fock (UHF) solutions are derived from this standpoint.