Braid map definition of SLH-networks and the series product

Abstract

This article investigates a cascade of quantum systems within an SLH-network. The original definition of an SLH-network depends on an open conjecture regarding the essential selfadjointness of the generator of the time evolution of the network. This problem is avoided by using the so-called braid-map, which leads to a rigorous definition of the SLH-network. An expression is derived for the time-evolution of the network with finite delay. The series product is recovered in the instantaneous feed-forward limit as a theorem that no longer depends on the conjecture.

arXiv comment6 pages, no figures