Quantum walk on a comb with infinite teeth

Abstract

We study continuous time quantum walk on a comb with infinite teeth and show that the return probability to the starting point decays with time t as t ⁻¹. We analyse the diffusion along the spine and into the teeth and show that the walk can escape into the teeth with a finite probability and goes to infinity along the spine with a finite probability. The walk along the spine and into the teeth behaves qualitatively as a quantum walk on a line. This behaviour is quite different from that of classical random walk on the comb.