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Continuous-time quantum walk on integer lattices and homogeneous trees
Vladislav Kargin · 2009-12-02 · via math.PR updates on arXiv.org

This paper is concerned with the continuous-time quantum walk on Z, Z^d, and infinite homogeneous trees. By using the generating function method, we compute the limit of the average probability distribution for the general isotropic walk on Z, and for nearest-neighbor walks on Z^d and infinite homogeneous trees. In addition, we compute the asymptotic approximation for the probability of the return to zero at time t in all these cases.

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