Notes on Inhomogeneous Quantum Walks
  We study a class of discrete-time quantum walks with inhomogeneous coins defined in [Y. Shikano and H. Katsura, Phys. Rev. E {\bf 82}, 031122 (2010)]. We establish symmetry properties of the spectrum of the evolution operator, which resembles the Hofstadter butterfly. 
Yutaka Shikano, Hosho Katsura
quant-ph cond-mat.dis-nn cond-mat.stat-mech math-ph math.MP