PreprintarXiv licencearXiv
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.
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BibTeX
@misc{bouten2026braid,
title = {{Braid map definition of SLH-networks and the series product}},
author = {Luc Bouten},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.13600},
eprint = {2609.13600},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13600},
}
RIS
TY - UNPB
TI - Braid map definition of SLH-networks and the series product
AU - Luc Bouten
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.13600
UR - https://arxiv.org/abs/2609.13600
AB - 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.
ER -