Balance between quantum Markov semigroups

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 partly motivated by the theory of joinings. Balance is defined in terms of certain correlated states (couplings), with entangled states as a specific case. Basic properties of balance are derived and the connection to correspondences in the sense of Connes is discussed. Some applications and possible applications, including to non-equilibrium statistical mechanics, are briefly explored.Comment: v1: 40 pages. v2: Corrections and small additions made, 41 page

Detailed balance and entanglement

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.National Research Foundation of South Africa.http://iopscience.iop.org0305-44702016-04-30hb201

Balance in W*-dynamical systems

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 states (couplings), with entangled states as a specific case. Basic properties of balance are derived, and a connection with correspondences in the sense of Connection is discussed. The characterization, and possible generalizations of a quantum detailed balance condition is explored. A characterization of ergodicity in terms of balance is also given.Thesis (PhD)--University of Pretoria, 2019.PhysicsPhDUnrestricte

Ergodic properties of noncommutative dynamical systems

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, and study C*-dynamical systems possessing these properties. Our analysis will show that, as in the classical case, only certain combinations of these properties are permissable on C*-dynamical systems. In the second half of this work, we construct concrete noncommutative C*-dynamical systems having various permissable combinations of the ergodic properties. This shows that, as in classical ergodic theory, these ergodic properties continue to be meaningful in the noncommutative case, and can be useful to classify and analyse C*-dynamical systems.Dissertation (MSc)--University of Pretoria, 2013.gm2014Mathematics and Applied Mathematicsunrestricte

Balance between quantum Markov semigroups

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 partly motivated by the theory of joinings. Balance is defined in terms of certain correlated states (couplings), with entangled states as a specific case. Basic properties of balance are derived, and the connection to correspondences in the sense of Connes is discussed. Some applications and possible applications, including to non-equilibrium statistical mechanics, are briefly explored.The National Research Foundation of South Africa.http://www.springer.com/birkhauser/physics/journal/232019-06-01hj2018Physic