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

Catalano, Alberto Giuseppe; Mattiotti, F.; Dubail, J.; Hagenmüller, D.; Prosen, T.; Franchini, Fabio; Pupillo, G. (2023) Anomalous Diffusion in the Long-Range Haken-Strobl-Reineker Model. Physical Review Letters, 131 (5). ISSN 0031-9007

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Official URL: http://doi.org/10.1103/PhysRevLett.131.053401

Abstract

We analyze the propagation of excitons in a d-dimensional lattice with power-law hopping ∝1/rα 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 αcr=(d+2)/2. The exciton always diffuses anomalously: a superdiffusive motion is associated to a Lévy stable distribution with long-range algebraic tails for α≤αcr, while for α>αcr 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 Lévy-flights. In the many-exciton case, we demonstrate that, starting from a domain-wall exciton profile, algebraic tails appear in the distributions for any α, 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.

Item Type:

Article

Uncontrolled Keywords:

Cold gases in optical lattices; Dipolar gases; Long-range interactions; Rydberg gases

Subjects:

NATURAL SCIENCES > Physics
NATURAL SCIENCES > Physics > Condensed Matter Physics

Divisions:

Theoretical Physics Division

Projects: