Continuous-time quantum walk on integer lattices and homogeneous trees
Probability
2015-05-14 v2 Mathematical Physics
math.MP
Quantum Physics
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.
Cite
@article{arxiv.0912.0232,
title = {Continuous-time quantum walk on integer lattices and homogeneous trees},
author = {Vladislav Kargin},
journal= {arXiv preprint arXiv:0912.0232},
year = {2015}
}
Comments
The journal version (save for formatting); 19 pages