16 research outputs found
Integral and fractional Quantum Hall Ising ferromagnets
We compare quantum Hall systems at filling factor 2 to those at filling
factors 2/3 and 2/5, corresponding to the exact filling of two lowest electron
or composite fermion (CF) Landau levels. The two fractional states are examples
of CF liquids with spin dynamics. There is a close analogy between the
ferromagnetic (spin polarization P=1) and paramagnetic (P=0) incompressible
ground states that occur in all three systems in the limits of large and small
Zeeman spin splitting. However, the excitation spectra are different. At
filling factor 2, we find spin domains at half-polarization (P=1/2), while
antiferromagnetic order seems most favorable in the CF systems. The transition
between P=0 and 1, as seen when e.g. the magnetic field is tilted, is also
studied by exact diagonalization in toroidal and spherical geometries. The
essential role of an effective CF-CF interaction is discussed, and the
experimentally observed incompresible half-polarized state is found in some
models
dftatom: A robust and general Schr\"odinger and Dirac solver for atomic structure calculations
A robust and general solver for the radial Schr\"odinger, Dirac, and
Kohn--Sham equations is presented. The formulation admits general potentials
and meshes: uniform, exponential, or other defined by nodal distribution and
derivative functions. For a given mesh type, convergence can be controlled
systematically by increasing the number of grid points. Radial integrations are
carried out using a combination of asymptotic forms, Runge-Kutta, and implicit
Adams methods. Eigenfunctions are determined by a combination of bisection and
perturbation methods for robustness and speed. An outward Poisson integration
is employed to increase accuracy in the core region, allowing absolute
accuracies of Hartree to be attained for total energies of heavy
atoms such as uranium. Detailed convergence studies are presented and
computational parameters are provided to achieve accuracies commonly required
in practice. Comparisons to analytic and current-benchmark density-functional
results for atomic number = 1--92 are presented, verifying and providing a
refinement to current benchmarks. An efficient, modular Fortran 95
implementation, \ttt{dftatom}, is provided as open source, including examples,
tests, and wrappers for interface to other languages; wherein particular
emphasis is placed on the independence (no global variables), reusability, and
generality of the individual routines.Comment: Submitted to Computer Physics Communication on August 27, 2012,
revised February 1, 201
Calculation of electron structure in the framework of DTF in real space
In the present work we study ab-initio electronic structure calculations in real space using density functional theory (DFT), finite elements and pseudopotentials. We summarize the theory and full ab-initio derivation of all equations in finite elements, density functional theory and pseudopotentials, then we explain how our program works and we show results for spherically symmetric potentials in relativistic and nonrelativistic DFT and for 2D and 3D Schrödinger equation for symmetric and non-symmetric potentials
Numerické řešení radiální Diracovy rovnice v konstrukci pseudopotenciálů
Ústav teoretické fyzikyInstitute of Theoretical PhysicsFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult
The virtual element method for eigenvalue problems with potential terms on polytopic meshes
summary:We extend the conforming virtual element method (VEM) to the numerical resolution of eigenvalue problems with potential terms on a polytopic mesh. An important application is that of the Schrödinger equation with a pseudopotential term. This model is a fundamental element in the numerical resolution of more complex problems from the Density Functional Theory. The VEM is based on the construction of the discrete bilinear forms of the variational formulation through certain polynomial projection operators that are directly computable from the degrees of freedom. The method shows a great flexibility with respect to the meshes and provides a correct spectral approximation with optimal convergence rates. This point is discussed from both the theoretical and the numerical viewpoint. The performance of the method is numerically investigated by solving the quantum harmonic oscillator problem with the harmonic potential and a singular eigenvalue problem with zero potential for the first eigenvalues
The Virtual Element Method for Eigenvalue Problems with Potential Terms on Polytopal Meshes
We extend the conforming virtual element method (VEM) to the numerical resolution of eigenvalue problems with potential terms on a polytopic mesh. An important application is that of the Schrödinger equation with a pseudopotential term. This model is a fundamental element in the numerical resolution of more complex problems from the Density Functional Theory. The VEM is based on the construction of the discrete bilinear forms of the variational formulation through certain polynomial projection operators that are directly computable from the degrees of freedom. The method shows a great flexibility with respect to the meshes and provides a correct spectral approximation with optimal convergence rates. This point is discussed from both the theoretical and the numerical view- point. The performance of the method is numerically investigated by solving the quantum harmonic oscillator problem with the harmonic potential and a singular eigenvalue problem with zero potential for the first eigenvalues