Quantum geodesic flows on graphs
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Volume
114
Publisher
DOI
10.1007/s11005-024-01860-6
Journal
Letters in Mathematical Physics
Issue
ISSN
0377-9017
Metadata
Show full item recordAbstract
We revisit the construction of quantum Riemannian geometries on graphs starting from a hermitian metric compatible connection, which always exists. We use this method to find quantum Levi-Civita connections on the n-leg star graph for n=2,3,4 and find the same phenomenon as recently found for the An Dynkin graph that the metric length for each inbound arrow has to exceed the length in the other direction by a multiple, here n. We then study quantum geodesics on graphs and construct these on the 4-leg graph and on the integer lattice line Z with a general edge-symmetric metric.