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Tuzaklanmış ultrasoğuk fermiyonlar için yoğunluk fonksiyoneli teorisi.

Akyar, Özge

Published Jan 1, 2009• 0 citations

Abstract

Recently a new outlook on dealing with dipolar ultracold fermions based on density functional methods has received attention. A Thomas-Fermi treatment coupled with a variational approach has been developed for a collection of fermions trapped in a harmonic potential interacting via dipole-dipole forces. In this thesis, firstly our alternative formalism for Thomas-Fermi method by performing some calculations based on the Kohn-Sham formalism which is one of the main idea of density functional theory is investigated. Furthermore, density distributions are obtained dependent to the parameters; rescaled interaction strength, dipole-dipole energy and the trap parameter which determine the trap geometry based on this theory. The thesis starts with a brief outline of the density functional theory and theory of our system, continues with calculations based on this theory, which are free of any variational assumptions for the density profile. Moreover, results of density graphics for harmonic trap will be followed by discussion of comparison and contrast with Thomas-Fermi method based on the paper of Goral et al.. These discussions are mainly about the shape of the density distribution, variation of the cloud parameters and energy behaviours according to the rescaled interaction strength. The thesis concludes with an analysis of contribution of density functional theory to this fermionic system.

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Recently a new outlook on dealing with dipolar ultracold fermions based on density functional methods has received attention. A Thomas-Fermi treatment coupled with a variational approach has been developed for a collection of fermions trapped in a harmonic potential interacting via dipole-dipole forces. In this thesis, firstly our alternative formalism for Thomas-Fermi method by performing some calculations based on the Kohn-Sham formalism which is one of the main idea of density functional theory is investigated. Furthermore, density distributions are obtained dependent to the parameters; rescaled interaction strength, dipole-dipole energy and the trap parameter which determine the trap geometry based on this theory. The thesis starts with a brief outline of the density functional theory and theory of our system, continues with calculations based on this theory, which are free of any variational assumptions for the density profile. Moreover, results of density graphics for harmonic trap will be followed by discussion of comparison and contrast with Thomas-Fermi method based on the paper of Goral et al.. These discussions are mainly about the shape of the density distribution, variation of the cloud parameters and energy behaviours according to the rescaled interaction strength. The thesis concludes with an analysis of contribution of density functional theory to this fermionic system.

We investigate the properties of a degenerate dilute gas of neutral fermionic particles in a harmonic trap that interact via dipole-dipole forces. We employ the semiclassical Thomas-Fermi method and discuss the Dirac correction to the interaction energy. A nearly analytic as well as an exact numerical minimization of the Thomas-Fermi-Dirac energy functional are performed in order to obtain the density distribution. We determine the stability of the system as a function of the interaction strength, the particle number, and the trap geometry. We find that there are interaction strengths and particle numbers for which the gas cannot be trapped stably in a spherically symmetric trap, but both prolate and oblate traps will work successfully.

We investigate the behavior of polarized dipolar fermions in a two-dimensional harmonic trap in the framework of the density functional theory (DFT) formalism using the local density approximation. We treat only a few particles interacting moderately. Important results were deduced concerning key characteristics of the system such as total energy and particle density. Our results indicate that, at variance with Coulombic systems, the exchange- correlation component was found to provide a large contribution to the total energy for a large range of interaction strengths and particle numbers. In addition, the density profiles of the dipoles are shown to display important features around the origin that is not possible to capture by earlier, simpler treatments of such systems.

Following the successful localization of dipolar ultracold atoms in harmonic traps, theoretical investigation of their density profiles have attracted very large interest in the literature. In this thesis, density functional theory will be used to investigate the density profiles of ultracold dipolar atoms (e.g. Cr) in harmonic potential traps. Parameters of the problem such as harmonic well depth, magnetic moments of the atoms will be explored in order to understand their effects on the density profile.

We systematically develop a density functional description for the equilibrium properties of a two-dimensional, harmonically trapped, spin-polarized dipolar Fermi gas based on the Thomas--Fermi--von Weizs\"acker approximation. We pay particular attention to the construction of the two-dimensional kinetic energy functional, where corrections beyond the local density approximation must be motivated with care. We also present an intuitive derivation of the interaction energy functional associated with the dipolar interactions and provide physical insight into why it can be represented as a local functional. Finally, a simple and highly efficient self-consistent numerical procedure is developed to determine the equilibrium density of the system for a range of dipole interaction strengths.

In this paper, we investigate the dynamical properties of a one-component Fermi gas with dipole–dipole interaction between particles. Using a variational function based on the Thomas–Fermi density distribution in phase space representation, the total energy is described as a function of deformation parameters in both real and momentum spaces. Various thermodynamic quantities of a uniform dipolar Fermi gas are derived, and then instability of this system is discussed. For a trapped dipolar Fermi gas, the collective oscillation frequencies are derived with the energy-weighted sum rule method. The frequencies for the monopole, quadrupole, radial and axial modes are calculated, and softening against collapse is shown as the dipolar strength approaches the critical value. Finally, we investigate the expansion dynamics of the Fermi gas and show how the dipolar interaction manifests itself in the shape of an expanded cloud.

We calculate the ground state energies of a system of two dipolar fermions trapped in a harmonic oscillator potential. The dipoles are assumed to be aligned parallel to each other. We perform the calculations of ground state energy as a function of strength of interaction between two fermions by employing variational method with Hylleraas-like explicitly correlated wave function. Furthermore, we perform calculations of ground state energy within Hartree-Fock approximation and the magnitude of correlation energy is estimated by subtracting these results from the corresponding wave function based results. We also carry out calculations of ground state energies within the realm of density functional theory by using recently reported expressions for exchange and correlation energies under local density approximation. By comparing correlated wave function based results with those obtained using density functional theory approach we examine the role of fermion-fermion correlation and assess the accuracy of local density approximation based expression for the correlation energy functional.