Academic literature on the topic 'One-dimensional and three-dimensional theory'

The GLuskap system for interactive three-dimensional graph drawing applies techniques of scientific visualization and interactive systems to the construction, display, and analysis of graph drawings. Important features of the system include support for large-screen stereographic 3D display with immersive head-tracking and motion-tracked interactive 3D wand control. A distributed rendering architecture contributes to the portability of the system, with user control performed on a laptop computer without specialized graphics hardware. An interface for implementing graph drawing layout and analysis algorithms in the Python programming language is also provided. This thesis describes comprehensively the work on the system by the author—this work includes the design and implementation of the major features described above. Further directions for continued development and research in cognitive tools for graph drawing research are also suggested.<br>viii, 110 leaves : ill. (some col.) ; 29 cm.

In this Dissertation thesis the spectral theory of Schrödinger operators modeling quasicrystals in dimension one ist investigated. We allow for a large class of measures as potentials covering also point interactions. The main results can be stated as follows: If the potential can be very well approximated by periodic potentials, then the correspondig Schrödinger operator does not have any eigenvalues. If the potential is aperiodic and satisfies a certain finite local complexity condition, the absolutely continuous spectrum is absent. We also prove Cantor spectra of zero Lebesgue measure for a large class of (a randomized version of) the operator.

In the past three decades, quasi-low-dimensional organic materials have attracted intense interests, both experimentally and theoretically. Due to their reduced dimensionality and relatively low carrier concentration, many organic materials exhibit strong electron correlations and numerous instabilities of the normal metallic state. The energy scales of such instabilities are often so low that the ground states can be changed by applying a reasonably strong magnetic field. Therefore, magnetic field is an effective tool for the study of quasi-low-dimensional organic materials. In this thesis, we will investigate two of these magnetic field related phenomena. In the first part, we will present our unified theory of angular magnetoresistance oscillations observed in organic conductors. We will demonstrate that, in spite of the absence of Landau level quantization for open Fermi surfaces in a magnetic field, a new quantum effect - Bragg reflections of electrons moving in the extended Brillouin zone - determines unusual magnetic properties of these materials. We will demonstrate that, at commensurate directions of a magnetic field, the electron motion shows 1D→2D dimensional crossover and leads to strong resistivity minima. We will present an analytic expression for interlayer resistivity, by both linear response formalism and solving the Boltzmann kinetic equation in the extended Brillouin zone. In two limiting cases, our general solution reduces to the results previously obtained for the LMA effects and LNL oscillations. We demonstrate that our theoretical results are in good qualitative and quantitative agreement with the existing measurements of resistivity in (TMTSF)₂ClO₄ conductor. In the second part, we will develop a theory for the recently observed high magnetic field high resistance state in (Per)₂Pt(mnt)₂. We demonstrate that the Pauli spinsplitting effects in a magnetic field improve nesting properties of a realistic quasi-onedimensional electron spectrum. As a result, a high resistance Peierls charge-density wave (CDW) phase is stabilized in high enough magnetic fields in (Per)₂Pt(mnt)₂ conductor. We show that, in low and very high magnetic fields, the Pauli spin-splitting effects lead to a stabilization of a soliton wall superlattice (SWS) CDW phase, which is characterized by periodically arranged soliton and anti-soliton walls. We suggest experimental studies of the predicted first order phase transitions between the Peierls and SWS phases to discover a unique SWS phase. It is important that, in the absence of a magnetic field and in a limit of very high magnetic fields, the suggested model is equivalent to the exactly solvable model of Brazovskii, Dzyaloshinskii, and Kirova.

Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2002.<br>Includes bibliographical references (leaves 105-110). Also available in electronic version. Access restricted to campus users.