Breakdown of an Electric-Field Driven System: A Mapping to a Quantum Walk

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 a delocalization transition occurs when the electric field is increased, which describes the dielectric breakdown in the original electron system.