Crossover between ballistic and diffusive transport: the quantum exclusion process

Author(s): V. Eisler

Journal: J. Stat. Mech.

Volume: 2011

Page(s): P06007

Year: 2011

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.


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