Hopf algebras, random walks and quantum master equations 1
Division of Mathematics, Department of Sciences Technical University of Crete, GR 731 00 Chania, Crete, Greece, E-mail: [email protected]
Received date: December 20, 2007; Revised date: March 31, 2008
Hopf algebras of functions and operators are utilized to develop a mathematical construction scheme for building algebraic random walks. The main construction treats systems of covariance formed by translation operator and its associated operator valued measures on e.g. the circle and the line, and derives an algebraic quantum random walk by means of completely positive trace preserving maps. Asymptotic limit of the action of such maps is shown to lead to quantum master equations of Lindblad type.