Search results for "Hartree"

Equilibrium properties of self-interacting neutrinos in the quasi-particle approach

2004

In this work a neutrino gas in equilibrium is studied both at T=0 and at finite temperature. Neutrinos are treated as massive Dirac quasi-particles with two generations. We include self-interactions among the neutrinos via neutral currents, as well as the interaction with a background of matter. To obtain the equilibrium properties we use Wigner function techniques. To account for corrections beyond the Hartree approximation, we also introduce correlation functions. We prove that, under the quasi-particle approximation, these correlation functions can be expressed as products of Wigner functions. We analyze the main properties of the neutrino eigenmodes in the medium, such as effective mass…

Relativistic Wigner function approach to neutrino propagation in matter

1999

In this work we study the propagation of massive Dirac neutrinos in matter with flavor mixing, using statistical techniques based on Relativistic Wigner Functions. First, we consider neutrinos in equilibrium within the Hartree approximation, and obtain the corresponding relativistic dispersion relations and effective masses. After this, we analyze the same system out of equilibrium. We verify that, under the appropiate physical conditions, the well known equations for the MSW effect are recovered. The techniques we used here appear as an alternative to describe neutrino properties and transport equations in a consistent way.

Quadrupole variation of projected spectra of even Ti isotopes

1975

In the present work we study the dependence of projected good $J$ states on the quadrupole moment. In order to achieve this, the quadrupole-moment-depenent generalized deformed BCS (DBCS) wave functions have been computed after minimizing the constrained Hamiltonian ${H}_{q}=H\ensuremath{-}\ensuremath{\lambda}N\ensuremath{-}\ensuremath{\mu}Q$. The calculation assumes the existence of a $^{40}\mathrm{Ca}$ spherical core. The two body residual interaction between the valence nucleons is determined by using the $^{42}\mathrm{Sc}$ spectrum for the $T=0$ force and the $^{49}\mathrm{Ca}$ spectrum for the $T=1$ force. The result of the calculation shows that the projected spectra in general cannot…

Time Dependent Hartree-Fock and Beyond

1983

Quantum corrections to the Wigner crystal: A Hartree-Fock expansion

1993

The quantum corrections to the two-dimensional Wigner crystal, for filling \ensuremath{\nu}\ensuremath{\le}1/3, are discussed by using a Hartree-Fock expansion based on wave functions which are (i) related to one another by magnetic translations, (ii) orthonormal, and (iii) strongly localized. Such wave functions are constructed in terms of Gaussians that are localized at the sites of a triangular (Wigner) lattice and have a small overlap c. The ground-state energy per particle is calculated by an expansion in \ensuremath{\surd}\ensuremath{\nu} and in \ensuremath{\delta}\ensuremath{\equiv}${\mathit{c}}^{1/4}$, which is rapidly convergent and stable under the thermodynamical limit. In partic…

Charge Distribution ofPb208and the Difference inρ(r)for Pb and Tl Investigated by by Elastic Electron Scattering

1976

Elastic electron-scattering cross sections from $^{208}\mathrm{Pb}$ have been measured for $0.5 {\mathrm{fm}}^{\ensuremath{-}1}lql2.24 {\mathrm{fm}}^{\ensuremath{-}1}$. The charge distribution for this nucleus is determined by a "model-independent" method; it exhibits a bump in the center of the nucleus which is also a characteristic feature of Hartree-Fock calculations. The influence of the $3s$ protons on $\ensuremath{\rho}(r)$ has been investigated by a difference measurement between lead and thallium isotones.

FFLO state in 1-, 2- and 3-dimensional optical lattices combined with a non-uniform background potential

2008

We study the phase diagram of an imbalanced two-component Fermi gas in optical lattices of 1-3 dimensions, considering the possibilities of the FFLO, Sarma/breached pair, BCS and normal states as well as phase separation, at finite and zero temperatures. In particular, phase diagrams with respect to average chemical potential and the chemical potential difference of the two components are considered, because this gives the essential information about the shell structures of phases that will occur in presence of an additional (harmonic) confinement. These phase diagrams in 1, 2 and 3 dimensions show in a striking way the effect of Van Hove singularities on the FFLO state. Although we focus o…

Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: a new v…

2012

We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic-oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (E…

Fe-periclase reactivity at Earth's lower mantle conditions: Ab-initio geochemical modelling

2017

Intrinsic and extrinsic stability of the (Mg, Fe) O solid mixture in the Fe-Mg-Si-O system at high P, T conditions relevant to the Earth's mantle is investigated by the combination of quantum mechanical calculations (Hartree-26 Fock/DFT hybrid scheme), cluster expansion techniques and statistical thermodynamics. Iron in the (Mg, Fe) O binary mixture is assumed to be either in the low spin (LS) or in the high spin (HS) state. Un-mixing at solid state is observed only for the LS condition in the 23-42 GPa pressure range, whereas HS does not give rise to un-mixing. LS (Mg, Fe) O un-mixings are shown to be able to incorporate iron by subsolidus reactions with a reservoir of a virtual bridgmanit…

Comparative Hybrid Hartree-Fock-DFT Calculations of WO2-Terminated Cubic WO3 as Well as SrTiO3, BaTiO3, PbTiO3 and CaTiO3 (001) Surfaces

2021

We greatly acknowledge the financial support via the ERAF Project No. 1.1.1.1/18/A/073. Calculations were performed using Latvian Super Cluster (LASC), located in the Center of Excellence at Institute of Solid State Physics, the University of Latvia, which is supported by European Union Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-Teaming Phase 2 under Grant Agreement No. 739508, project CAMART.