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Department of Physics and Astronomy Quantum Chaos Research

Ph.D. Theses

Role of dynamics in interacting fermion systems: The Strutinsky method and ground state properties of quantum dots

by Nagano, Tatsuro, Ph.D., Washington State University, 2002 , 247 pages [Thesis (7.3 MB)]

Abstract (Summary) We investigate nano-structure quantum dots which show conductance peak oscillations in the Coulomb blockade regime. Although a random matrix theoretical approach (RMT) has made successful predictions, the statistical behaviors of the peak spacings remain mysterious, indicating the necessity of a more subtle treatment of the residual interaction. We pursue a many-body framework, which explicitly includes electron-electron interaction in the context of density functional theory. Based on the idea of the Strutinsky shell correction method, the ground state energy is expressed by an approximate series expansion in the fluctuation part of the density functional, and the physical interpretation of each successive term is analyzed. We identify the energy contribution of the residual interaction due to the screened Coulomb potential. Given that irregularly shaped quantum clots consist of quasiparticles interacting through a screened Coulomb interaction, we employ the two-dimensional coupled quartic oscillator as an effective confinement. The advantage of employing the quartic oscillator is that the degree of chaos can be tuned continuously from integrability to pure chaos, allowing us to study how the nature of the dynamics influences the single-particle orbital occupancies when spin is taken into account. In the analysis of the ground state configuration and spin polarization, the conductance peak spacings are reproduced and the electron orbital occupations are observed to depend upon the nature of the dynamics. The greater the chaos, the less effective the residual interaction in altering the occupations.