Quantum transport properties of electron systems driven by strong electric fields are studied by mapping the Landau-Zener transition dynamics to a quantum walk on a semi-infinite one-dimensional lattice with a reflecting boundary, where the sites correspond to energy levels and the boundary the ground state. Quantum interference induces a distribution localized around the ground state, and when the electric field is strengthened, a delocalization transition occurs describing breakdown of the original electron system.
@article{arxiv.quant-ph/0407013,
title = {Breakdown of an Electric-Field Driven System: a Mapping to a Quantum Walk},
author = {Takashi Oka and Norio Konno and Ryotaro Arita and Hideo Aoki},
journal= {arXiv preprint arXiv:quant-ph/0407013},
year = {2016}
}