0 CONTINUOUS-TIME QUANTUM WALK ON INTEGER LATTICES AND HOMOGENEOUS TREES
Vladislav Kargin · 2016
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.