Test of Density Functional Approximation for an Atom in a Strong Magnetic Field

Shiwei Li, Jerome K. Percus

A density-functional model of atoms in strong magnetic fields is proposed along lines parallel to Hohenberg-Kohn-Sham density-functional theory. We derive a Thomas-Fermi-Weiz\"acker-like (TFW) functional by using the classical-path approximation to the relevant one-particle Green's function. We also address the correlation effect between the effective potential and the magnetic field. The TFW-like model provides a simple way of calculating ground-state energies and charge densities of atoms in magnetic fields, and can be systematically improved.

Francesc Malet, André Mirtschink, Klaas J. H. Giesbertz +1 more

Sami Siljamaki

This thesis investigates the use of wave-function methods for the study of quantum-dot systems. It investigates single dots, using quantum Monte Carlo techniques in a wide range of magnetic field values, and a double-dot system, using the exact-diagonalization method.\n\nThe thesis proposes simple yet accurate many-particle wave functions for various angular-momentum and spin states, for both weak and strong magnetic fields. Using these trial wave functions, it evaluates various properties of dots and studies Wigner crystallization and spin polarization for the weak-field limit. For strong magnetic fields, the thesis investigates ground states of different spin polarizations as a function of the magnetic field and tests the commonly used lowest-Landau-level approximation. The results are compared to calculations from the density-functional theory.\n\nFinally, the thesis presents a method that combines the accuracy of the exact-diagonalization method and the scalability of Monte Carlo methods. The Monte Carlo-based diagonalization is a promising tool for use in situations that cannot be handled with a simple trial wave function, and have too many particles for an exact-diagonalization treatment. For quantum dots, methods for efficiently evaluating the high-magnetic-field basis functions and their gradients are demonstrated.

Swapan K. Ghosh

Moritz Braun

Results of density-functional calculations for atoms in very strong magnetic fields using a two-dimensional finite-element basis set are reported for ground-state energies of helium, carbon, and neon, and for some excited states of helium. We give results obtained by using three different local-density functionals. A comparison with multi-Landau-channel Hartree-Fock calculations shows reasonable agreement for helium.

Axel D. Becke