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arXiv · 2312.10779

Quantum geodesic flows on graphs

Edwin Beggs·Shahn Majid
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Abstract

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 $A_n$ Dynkin graph that the metric length for each outbound arrow has to exceed the length in the other direction by a multiple, here $\sqrt{n}$. We then study quantum geodesics on graphs and construct these on the 4-leg graph and on the integer lattice line $\Bbb Z$ with a general edge-symmetric metric

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Edwin Beggs, Shahn Majid. 2023-12-17. Quantum geodesic flows on graphs. https://arxiv.org/abs/2312.10779

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