Levinson's theorem for graphs

Abstract

We prove an analog of Levinson's theorem for scattering on a weighted (m+1)-vertex graph with a semi-infinite path attached to one of its vertices. In particular, we show that the number of bound states in such a scattering problem is equal to m minus half the winding number of the phase of the reflection coefficient (where each so-called half-bound state is counted as half a bound state).

10 pages, 1 figure; v2: minor corrections

References in corpus (4)

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

Cited by in corpus (7)

• Levinson's theorem for graphs II
• Towards Quantum Computing with Molecular Electronics
• Quantum Slide and NAND Tree on a Photonic Chip
• Molecular Realization of a Quantum NAND Tree
• The spectral shift function and Levinson's theorem for quantum star graphs
• Momentum switches
• Many-Body Effects in a Molecular Quantum NAND Tree