Every finite cyclic quantum history is classified by the monodromy of its unitary steps, and the exact spectrum, zero-energy sector, and minimal clock rules follow from that one operator.
Matching number, Hamiltonian graphs and discrete magnetic Laplacians
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abstract
In this article, we relate the spectrum of the discrete magnetic Laplacian (DML) on a finite simple graph with two structural properties of the graph: the existence of a perfect matching and the existence of a Hamiltonian cycle of the underlying graph. In particular, we give a family of spectral obstructions parametrised by the magnetic potential for the graph to be matchable (i.e., having a perfect matching) or for the existence of a Hamiltonian cycle. We base our analysis on a special case of the spectral preorder introduced in [FCLP20a] and we use the magnetic potential as a spectral control parameter.
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Finite Quantum Histories: Holonomy Spectra, Minimal Clocks, and Exact Clock-Change Covariance
Every finite cyclic quantum history is classified by the monodromy of its unitary steps, and the exact spectrum, zero-energy sector, and minimal clock rules follow from that one operator.