Quantum random walks and thermalisation II
Abstract
A convergence theorem is obtained for quantum random walks with particles in an arbitrary normal state. This result unifies and extends previous work on repeated-interactions models, including that of the author (2010, J. London Math. Soc. (2) 81, 412-434; 2010, Comm. Math. Phys. 300, 317-329). When the random-walk generator acts by ampliation and multiplication or conjugation by a unitary operator, necessary and sufficient conditions are given for the quantum stochastic cocycle which arises in the limit to be driven by an isometric, co-isometric or unitary process.
Cite
@article{arxiv.1209.5059,
title = {Quantum random walks and thermalisation II},
author = {Alexander C. R. Belton},
journal= {arXiv preprint arXiv:1209.5059},
year = {2012}
}
Comments
28 pages. This version has an expanded introduction and contains a new section, where the main theorem is applied to show that certain quantum random walks converge to unitary Hudson-Parathasarthy evolutions and inner Evans-Hudson flows; minor revisions have been made to the rest of the text