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In this note, we consider a physical system given by a two-dimensional quantum walk in an external magnetic field. In this setup, we show that both the topological structure as well as its type depend sensitively on the value of the magnetic flux $Phi$: while for $Phi/(2{pi})$ rational the spectrum is known to consist of bands, we show that for $Phi/(2{pi})$ irrational the spectrum is a zero-measure Cantor set and the spectral measures have no pure point part.
In this paper we present a model exhibiting a new type of continuous-time quantum walk (as a quantum mechanical transport process) on networks, which is described by a non-Hermitian Hamiltonian possessing a real spectrum. We call it pseudo-Hermitian
Given its importance to many other areas of physics, from condensed matter physics to thermodynamics, time-reversal symmetry has had relatively little influence on quantum information science. Here we develop a network-based picture of time-reversal
We consider the Grover walk on infinite trees from the view point of spectral analysis. From the previous works, infinite regular trees provide localization. In this paper, we give the complete characterization of the eigenspace of this Grover walk,
We study a spin-1/2-particle moving on a one dimensional lattice subject to disorder induced by a random, space-dependent quantum coin. The discrete time evolution is given by a family of random unitary quantum walk operators, where the shift operati
In this paper, we consider the quantum walk on $mathbb{Z}$ with attachment of one-length path periodically. This small modification to $mathbb{Z}$ provides localization of the quantum walk. The eigenspace causing this localization is generated by fin