C. M. Chandrashekar, Th. Busch
Quantum percolation describes the problem of a quantum particle moving through a randomly frozen medium. While certain similarities to classical percolation exist, the dynamics of quantum percolation has additional complexity due to the possibility of Anderson localization. Here we show that this strongly influences the percolations threshold by considering a directed two-state quantum walk on a two dimensional space. To do this we determine the Anderson transition point (the quantum equivalent to the classical percolation threshold) for three fundamental lattice geometries (finite square lattice, honeycomb lattice, and nanotube structure) and show that it differs significantly from the classical value and tends towards unity for increasing lattice sizes. Beyond the fundamental interest for understanding the dynamics of a two-state particle on the lattice (network) with disconnected vertices, our study also sheds light on the transport dynamics in various quantum condensed matter systems and the construction of several quantum information processing and communication protocols.
View original:
http://arxiv.org/abs/1303.7013
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