Browsing Physics by Author "Duvenhage, Rocco de Villiers"

Browsing Physics by Author "Duvenhage, Rocco de Villiers"

Sort by: Order: Results:

  • Analyticity and spectral properties of noncommutative Ricci flow in a matrix geometry 
    Duvenhage, Rocco de Villiers; Van Staden, Wernd; Wuzyk, Jan (Elsevier, 2018-02)
    We study a first variation formula for the eigenvalues of the Laplacian evolving under the Ricci flow in a simple example of a noncommutative matrix geometry, namely a finite dimensional representation of a noncommutative ...
  • Balance between quantum Markov semigroups 
    Duvenhage, Rocco de Villiers; Snyman, Machiel (Springer, 2018-06)
    The concept of balance between two state-preserving quantum Markov semigroups on von Neumann algebras is introduced and studied as an extension of conditions appearing in the theory of quantum detailed balance. This is ...
  • C∗ -fermi systems and detailed balance 
    Crismale, Vitonofrio; Duvenhage, Rocco de Villiers; Fidaleo, Francesco (Springer, 2021-03)
    Please read abstract in the article.
  • Detailed balance and entanglement 
    Duvenhage, Rocco de Villiers; Snyman, Machiel (IOP Publishing, 2015-04)
    We study a connection between quantum detailed balance, which is a concept of importance in statistical mechanics, and entanglement. We also explore how this connection ts into thermo eld dynamics.
  • Disjointness of C-dynamical systems 
    Duvenhage, Rocco de Villiers; Stroh, Anton (University of Houston, Houston, Texas, 2016)
    We study ergodic theorems for disjoint C*- and W*-dynamical systems, where disjointness here is a noncommutative version of the concept introduced by Furstenberg for classical dynamical systems. We also consider speci ...
  • Ergodicity and mixing of W*-dynamical systems in terms of joinings 
    Duvenhage, Rocco de Villiers (Department of Mathematics, University of Illinois, 2011)
    We study characterizations of ergodicity, weak mixing and strong mixing of W*-dynamical systems in terms of joinings and subsystems of such systems. Ergodic joinings and Ornstein’s criterion for strong mixing are also ...
  • Fermionic quantum detailed balance and entanglement 
    Duvenhage, Rocco de Villiers (IOP Publishing, 2018-08)
    A definition of detailed balance, tailored to a system of indistinguishable fermions, is suggested and studied using an entangled fermionic state. This is done in analogy to a known characterization of standard quantum ...
  • Free joinings of C-dynamical systems 
    Duvenhage, Rocco de Villiers (Elsevier, 2010-04)
    Joinings of C∗-dynamical systems are defined in terms of free products of C∗-algebras, as an analogue of joinings of classical dynamical systems. We then consider disjointness in this context, in particular for ergodic ...
  • Noncommutative Ricci flow in a matrix geometry 
    Duvenhage, Rocco de Villiers (Institute of Physics, 2014-01)
    We study noncommutative Ricci flow in a finite-dimensional representation of a noncommutative torus. It is shown that the flow exists and converges to the flat metric. We also consider the evolution of entropy and a ...
  • Optimal quantum channels 
    Duvenhage, Rocco de Villiers (American Physical Society, 2021-09-07)
    A method to optimize the cost of a quantum channel is developed. The goal is to determine the cheapest channel that produces prescribed output states for a given set of input states. This is essentially a quantum version ...
  • Quantum Wasserstein distance of order 1 between channels 
    Duvenhage, Rocco de Villiers; Mapaya, Mathumo (World Scientific Publishing, 2023-06)
    We set up a general theory leading to a quantum Wasserstein distance of order 1 between channels in an operator algebraic framework. This gives a metric on the set of channels from one composite system to another, which ...
  • Relative discrete spectrum of W*-dynamical system 
    Duvenhage, Rocco de Villiers; King, Malcolm (Springer, 2021-01)
    A definition of relative discrete spectrum of noncommutative W*-dynamical systems is given in terms of the basic construction of von Neumann algebras, motivated from three perspectives: First, as a complementary concept ...
  • Relative ergodic properties of C*-dynamical systems 
    Duvenhage, Rocco de Villiers; Mukhamedov, Farrukh (World Scientific Publishing, 2014-03)
    We study various ergodic properties of C*-dynamical systems inspired by unique ergodicity. In particular we work in a framework allowing for ergodic properties defined relative to various subspaces, and in terms of ...
  • Relative weak mixing of W∗-dynamical systems via joinings 
    Duvenhage, Rocco de Villiers; King, Malcolm (Polish Academy of Sciences, Institute of Mathematics, 2019)
    A characterization of relative weak mixing in W∗-dynamical systems in terms of a relatively independent joining is proven.
  • Relatively independent joinings and subsystems of W*-dynamical systems 
    Duvenhage, Rocco de Villiers (Polskiej Akademii Nauk, Instytut Matematyczny, 2012)
    Relatively independent joinings ofW*-dynamical systems are constructed. This is intimately related to subsystems of W*-dynamical systems, and therefore we also study general properties of subsystems, in particular fixed ...