Quantum random walks and thermalisation

Belton, Alexander C. R. (2010) Quantum random walks and thermalisation. Communications in Mathematical Physics, 300 (2). pp. 317-329. ISSN 0010-3616

Abstract

It is shown how to construct quantum random walks with particles in an arbitrary faithful normal state. A convergence theorem is obtained for such walks, which demonstrates a thermalisation effect: the limit cocycle obeys a quantum stochastic differential equation without gauge terms. Examples are presented which generalise that of Attal and Joye (J Funct Anal 247:253–288, 2007).