We develop a semiclassical density functional theory in the context of quantum dots. Coulomb blockade conductance oscillations have been measured in several experiments using nanostructured quantum dots. The statistical properties of these oscillations remain puzzling, however, particularly the statistics of spacings between conductance peaks. To explore the role that residual interactions may play in the spacing statistics, we consider many-body systems which include electron-electron interactions through an explicit density functional. First, we develop an approximate series expansion for obtaining the ground state using the idea of the Strutinsky shell correction method. Next, we relate the second-order semiclassical corrections to the screened Coulomb potential. Finally, we investigate the validity of the approximation method by numerical calculation of a one-dimensional model system, and show the relative magnitudes of the successive terms as a function of particle number.
We consider how the nature of the dynamics affects ground state properties of ballistic quantum dots. We find that "mesoscopic Stoner fluctuations", that arise from the residual screened Coulomb interaction, are very sensitive to the degree of chaos. It leads to ground state energies and spin-polarizations whose fluctuations strongly increase as a system becomes less chaotic. The crucial features are illustrated with a model that depends on a parameter that tunes the dynamics from nearly integrable to mostly chaotic.Our interest in this letter lies in microstructures fabricated using electrostatic gates or etching that pattern a two dimensional electron gas in a semiconductor heterostructure, for example, GaAs/AlGaAs. Typically, the electronic transport mean free path is significantly larger than the dimensions of the device, and the electrons essentially travel ballistically across the microstructure. Their motion is governed by the shape of a smooth, self-consistent, steep-walled, confining potential which is often conceptualized as a quantum billiard.For many physical properties, the simplifying assumption that the dots' underlying classical dynamics are fully chaotic (hard chaos) has provided a good description of the experimental data [1,2,3,4]. It has been used to justify various hypotheses from the applicability of random matrix theory (RMT) and random plane wave modeling (RPW) to statistical assumptions applied within semiclassical mechanics [5,6,7]. Indeed, chaotic systems manifest a large variety of universal behaviors. Furthermore, chaotic quantum dots are often qualitatively very similar to diffusive ones provided the Thouless energy E T H is defined ashv F /L, where v F is the Fermi velocity and L is a typical dimension of the dot (as opposed tō hD/L 2 with D the diffusion constant). Consequently, most techniques, developed much earlier to study disordered metals (diagrammatic approaches [8], nonlinear sigma model [9]) and applied to disordered quantum dots [10,11,12], are applicable to ballistic quantum dots.Nevertheless, unlike billiards, there are no known smooth potentials which are truly, fully chaotic. Unless designed otherwise for a specific purpose (such as measuring the weak localization lineshape [13]) an odd-shaped, smooth potential generically exhibits soft chaos, i.e. significant contributions of both stable and unstable motion. The general assumption of hard chaos is unfounded.As opposed to a genuine belief that the electrons' dynamics are strongly chaotic, the implicit assumption is that for many properties the distinctions between soft and hard chaos are more subtle than spectacular. This has been shown explicitly, for instance, for the fluctuation properties of Coulomb blockade (CB) peak heights [14], or for their correlations [15]. In such circumstances, using a chaotic model allows for simpler analytic derivations without drastically altering the results.Our purpose here is to demonstrate that even this weaker assumption may, in some cases, be problematic; and that for some proper...
We consider how the nature of the dynamics affects ground state properties of ballistic quantum dots. We find that "mesoscopic Stoner fluctuations", that arise from the residual screened Coulomb interaction, are very sensitive to the degree of chaos. It leads to ground state energies and spin-polarizations whose fluctuations strongly increase as a system becomes less chaotic. The crucial features are illustrated with a model that depends on a parameter that tunes the dynamics from nearly integrable to mostly chaotic.Our interest in this letter lies in microstructures fabricated using electrostatic gates or etching that pattern a two dimensional electron gas in a semiconductor heterostructure, for example, GaAs/AlGaAs. Typically, the electronic transport mean free path is significantly larger than the dimensions of the device, and the electrons essentially travel ballistically across the microstructure. Their motion is governed by the shape of a smooth, self-consistent, steep-walled, confining potential which is often conceptualized as a quantum billiard.For many physical properties, the simplifying assumption that the dots' underlying classical dynamics are fully chaotic (hard chaos) has provided a good description of the experimental data [1,2,3,4]. It has been used to justify various hypotheses from the applicability of random matrix theory (RMT) and random plane wave modeling (RPW) to statistical assumptions applied within semiclassical mechanics [5,6,7]. Indeed, chaotic systems manifest a large variety of universal behaviors. Furthermore, chaotic quantum dots are often qualitatively very similar to diffusive ones provided the Thouless energy E T H is defined ashv F /L, where v F is the Fermi velocity and L is a typical dimension of the dot (as opposed tō hD/L 2 with D the diffusion constant). Consequently, most techniques, developed much earlier to study disordered metals (diagrammatic approaches [8], nonlinear sigma model [9]) and applied to disordered quantum dots [10,11,12], are applicable to ballistic quantum dots.Nevertheless, unlike billiards, there are no known smooth potentials which are truly, fully chaotic. Unless designed otherwise for a specific purpose (such as measuring the weak localization lineshape [13]) an odd-shaped, smooth potential generically exhibits soft chaos, i.e. significant contributions of both stable and unstable motion. The general assumption of hard chaos is unfounded.As opposed to a genuine belief that the electrons' dynamics are strongly chaotic, the implicit assumption is that for many properties the distinctions between soft and hard chaos are more subtle than spectacular. This has been shown explicitly, for instance, for the fluctuation properties of Coulomb blockade (CB) peak heights [14], or for their correlations [15]. In such circumstances, using a chaotic model allows for simpler analytic derivations without drastically altering the results.Our purpose here is to demonstrate that even this weaker assumption may, in some cases, be problematic; and that for some proper...
3 dimensional computer graphics (3DCG) becomes an easily accessible technology for general public. Average PC users can design and embed high quality 3DCG images and animations in their work. They must, however, study text books and related web pages with captured 2D images for understanding 3DCG theories and graphics programming to become a good designer. They must also master complex 3D operations specific to a dedicated software tool for acquiring appropriate authoring skills. These efforts require enormous amount of time and impose a heavy burden on the users. To solve the problem, we have been developing a 3DCG learning support system enabling the users to intuitively acquire knowledge and skills necessary for 3DCG contents authoring and graphics programming. In this paper, we describe the concept, implementation method, and evaluation of the proposed system.
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