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Quantum geodesic flows on graphs
- Publication Year :
- 2023
-
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<br />Comment: 29 pages latex, 5 pdf figures
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2312.10779
- Document Type :
- Working Paper