Levinson's theorem for graphs II

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.

Published version

References in corpus (5)

• Quantum Computation and Decision Trees
• Universal computation by quantum walk
• Exponential algorithmic speedup by quantum walk
• Quantum scattering theory on graphs with tails
• Levinson's theorem for graphs

Cited by in corpus (12)

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• Two-level Quantum Walkers on Directed Graphs I: Universal Quantum Computing
• Two-Particle Scattering on Non-Translation Invariant Line Lattices
• Momentum switches
• Schroedinger wave operators on the discrete half-line
• Many-Body Effects in a Molecular Quantum NAND Tree
• Two-particle scattering on general graphs