Crossover between ballistic and diffusive transport: the quantum exclusion process
Author(s): V. Eisler
Journal: J. Stat. Mech.
DOI Number: 10.1088/1742-5468/2011/06/P06007
Link: Link to publication
We study the evolution of a system of free fermions in one dimension under the simultaneous effects of coherent tunneling and stochastic Markovian noise. We identify a class of noise terms where a hierarchy of decoupled equations for the correlation functions emerges. In the special case of incoherent, nearest-neighbor hopping the equation for the two-point functions is solved explicitly. The Green's function for the particle density is obtained analytically and a time scale is identified where a crossover from ballistic to diffusive behavior takes place. The result can be interpreted as a competition between the two types of conduction channels where diffusion dominates on large timescales.Note: http://arxiv.org/abs/1104.4050 File: Link to PDF