Anomalous Diffusion in the Long-Range Haken-Strobl-Reineker Model

We analyze the propagation of excitons in a d -dimensional lattice with power-law hopping cc 1/ra in the presence of dephasing, described by a generalized Haken-Strobl-Reineker model. We show that in the strong dephasing (quantum Zeno) regime the dynamics is described by a classical master equation for an exclusion process with long jumps. In this limit, we analytically compute the spatial distribution, whose shape changes at a critical value of the decay exponent a(cr) = (d + 2)/2. The exciton always diffuses anomalously: a superdiffusive motion is associated to a Levy stable distribution with long-range algebraic tails for a = acr, while for a > a(cr) the distribution corresponds to a surprising mixed Gaussian profile with long-range algebraic tails, leading to the coexistence of short-range diffusion and long-range Levy flights. In the many-exciton case, we demonstrate that, starting from a domain-wall exciton profile, algebraic tails appear in the distributions for any a, which affects thermalization: the longer the hopping range, the faster equilibrium is reached. Our results are directly relevant to experiments with cold trapped ions, Rydberg atoms, and supramolecular dye aggregates. They provide a way to realize an exclusion process with long jumps experimentally.