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5 papers · 2 filters
Quantum walks and elliptic integrals
Norio Konno
Polya showed in his 1921 paper that the generating function of the return probability for a two-dimensional random walk can be written in terms of an elliptic integral. In this pap…
Localization of an inhomogeneous discrete-time quantum walk on the line
Norio Konno
We investigate a space-inhomogeneous discrete-time quantum walk in one dimension. We show that the walk exhibits localization by a path counting method.
One-dimensional discrete-time quantum walks on random environments
Norio Konno
We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed w…
Limit theorems for discrete-time quantum walks on trees
Kota Chisaki, Masatoshi Hamada, Norio Konno +1
We consider a discrete-time quantum walk W_t given by the Grover transformation on the Cayley tree. We reduce W_t to a quantum walk X_t on a half line with a wall at the origin. Th…
Orthogonal polynomials induced by discrete-time quantum walks in one dimension
Masatoshi Hamada, Norio Konno, Wojciech Mlotkowski
In this paper we obtain some properties of orthogonal polynomials given by a weight function which is a limit density of a rescaled discrete-time quantum walk on the line.