My progress reports may have been dormant for a few weeks, but the search for Levinson’s theorem on graphs has not! Â (My laptop was stolen last week so my recent time with computers has been necessarily precious and could not be wasted on blog ramblings. Â More on this below.) Explorations in Mathematica As you may [...]
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My recent hacks at trying to find the scattering and bound states of a semi-infinite line attached to a single weighted edge (the simplest graph imaginable) hadn’t been too successful until today. I had not really been sure about how to approach the problem and had only written down a Hamiltonian and postulated some qualitative [...]
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This morning I had a call with IQC’s Andrew Childs and we pinned down our summer project. The goal is to investigate the analog of “Levinson’s theorem” (originally formulated for general scattering problems) for the case of scattering on graphs. Levinson’s theorem basically relates the phase shift of a scattered state to the bound states [...]
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