Continuous-time quantum walk on integer lattices and homogeneous trees

Abstract

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.

The journal version (save for formatting); 19 pages

References in corpus (4)

• Quantum random walks - an introductory overview
• Weak limits for quantum random walks
• Limit Theorem for Continuous-Time Quantum Walk on the Line
• Convergence of continuous-time quantum walks on the line

Cited by in corpus (1)

• Quantum walks: a comprehensive review