Levinson's theorem for graphs
Mathematical Physics
2011-08-12 v2 math.MP
Quantum Physics
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).
Cite
@article{arxiv.1103.5077,
title = {Levinson's theorem for graphs},
author = {Andrew M. Childs and DJ Strouse},
journal= {arXiv preprint arXiv:1103.5077},
year = {2011}
}
Comments
10 pages, 1 figure; v2: minor corrections