Browsing by Supervisor "Duvenhage, Rocco"

Browsing by Supervisor "Duvenhage, Rocco"

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  • Balance in W*-dynamical systems 
    Snyman, Mathys Machiel (University of Pretoria, 2019)
    Using a study of the connection between entanglement and quantum detailed balance as motivation, we define and study the concept of balance between two W -dynamical systems. Balance is defined in terms of certain correlated ...
  • A dynamical approach to quantum optimal transport 
    Mare, Chantel (University of Pretoria, 2021)
    We begin with a brief overview of measure theory and the theory of optimal transport. We then proceed to study a special class of quantum states represented by quantum Markov semi-groups (QMS) on a finite dimensional ...
  • Ergodic properties of noncommutative dynamical systems 
    Snyman, Mathys Machiel (University of Pretoria, 2013)
    In this dissertation we develop aspects of ergodic theory for C*-dynamical systems for which the C*-algebras are allowed to be noncommutative. We define four ergodic properties, with analogues in classic ergodic theory, ...
  • Joinings and relative ergodic properties of W*-dynamical systems 
    King, Malcolm Bruce (University of Pretoria, 2019)
    We prove a characterization of relative weak mixing in W*-dynamical systems in terms of a relatively independent joining. We then define a noncommutative version of relative discrete spectrum, show that it generalizes both ...
  • Metric aspects of noncommutative geometry 
    van Staden, Wernd Jakobus (University of Pretoria, 2019)
    We study noncommutative geometry from a metric point of view by constructing examples of spectral triples and explicitly calculating Connes's spectral distance between certain associated pure states. After considering ...
  • A noncommutative sigma model 
    Van den Worm, Mauritz (University of Pretoria, 2012-10-11)
    We replaced the classical string theory notions of parameter space and world-time with noncommutative tori and consider maps between these spaces. The dynamics of mappings between different noncommutative tori were studied ...
  • Operator algebras and quantum information 
    Oerder, Kyle (University of Pretoria, 2020-05)
    The C*-algebra representation of a physical system provides an ideal backdrop for the study of bipartite entanglement, as a natural definition of separability emerges as a direct consequence of the non-abelian nature of ...
  • A structure theorem for asymptotically abelian W*-dynamical systems 
    King, Malcolm Bruce (University of Pretoria, 2016)
    We prove a partial non-commutative analogue of the Furstenberg-Zimmerman Structure Theorem, originally proved by Tim Austin, Tanya Eisner and Terence Tao. In Chapter 1, we review the GNS construction for states on von ...
  • The Szemerédi property in noncommutative dynamical systems 
    Beyers, Frederik Johannes Conradie (University of Pretoria, 2009-06-02)
    No abstract available. Copyright 2008, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by ...
  • Tomita-Takesaki theory in B(H) with physical applications 
    Skosana, Samuel (University of Pretoria, 2019)
    The main aim of this project is to develop a simple, yet mathematically rigorous, version of Tomita-Takesaki theory for the von Neumann algebra B(H ) with a faithful normal state. In Chapter 2 we formulate the theory in ...
  • Unique ergodicity in C*-dynamical systems 
    Van Wyk, Daniel Willem (University of Pretoria, 2013)
    The aim of this dissertation is to investigate ergodic properties, in particular unique ergodicity, in a noncommutative setting, that is in C*-dynamical systems. Fairly recently Abadie and Dykema introduced a broader ...