Changing gears: Isospectrality via eigenderivative transplantation
Peter Doyle, Peter Herbrich
TL;DR
This paper introduces a novel method for creating isospectral quantum graphs using eigenderivative transplantation and explores digraphs with identical reversing zeta functions, extending spectral graph theory.
Contribution
It presents a new eigenderivative transplantation technique for isospectral quantum graphs and generalizes the Bartholdi zeta function to digraphs.
Findings
Constructed new isospectral quantum graphs using eigenderivative transplantation
Identified digraphs with identical reversing zeta functions
Extended the Bartholdi zeta function to directed graphs
Abstract
We introduce a new method for constructing isospectral quantum graphs that is based on transplanting derivatives of eigenfunctions. We also present simple digraphs with the same reversing zeta function, which generalizes the Bartholdi zeta function to digraphs.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum and electron transport phenomena