Derives scattering matrix formulas for quantum walks on two-lead graphs and characterizes perfect transmission via additive quantities μ1, μ2, ν under parallel composition.
Levinson's theorem for graphs II
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abstract
We prove Levinson's theorem for scattering on an (m+n)-vertex graph with n semi-infinite paths each attached to a different vertex, generalizing a previous result for the case n=1. This theorem counts the number of bound states in terms of the winding of the determinant of the S-matrix. We also provide a proof that the bound states and incoming scattering states of the Hamiltonian together form a complete basis for the Hilbert space, generalizing another result for the case n=1.
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2026 1verdicts
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Perfect transmission and parallel composition for quantum walks on graphs with two leads
Derives scattering matrix formulas for quantum walks on two-lead graphs and characterizes perfect transmission via additive quantities μ1, μ2, ν under parallel composition.