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arXiv · 2212.07744

Anomalous diffusion in the Long-Range Haken-Strobl-Reineker model

Alberto Giuseppe Catalano·Francesco Mattiotti·Jérôme Dubail·David Hagenmüller·Tomaž Prosen·Fabio Franchini·Guido Pupillo
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Abstract

We analyze the propagation of excitons in a $d$-dimensional lattice with power-law hopping $\propto 1/r^\alpha$ 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 $\alpha_{\rm cr} = (d+2)/2$. The exciton always diffuses anomalously: a superdiffusive motion is associated to a L\'evy stable distribution with long-range algebraic tails for $\alpha\leq\alpha_{\rm cr}$, while for $\alpha > \alpha_{\rm cr}$ 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 L\'evy-flights. In the many-exciton case, we demonstrate that, starting from a domain-wall exciton profile, algebraic tails appear in the distributions for any $\alpha$, 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.

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Alberto Giuseppe Catalano, Francesco Mattiotti, Jérôme Dubail, David Hagenmüller, Tomaž Prosen, Fabio Franchini, Guido Pupillo. 2022-12-15. Anomalous diffusion in the Long-Range Haken-Strobl-Reineker model. https://doi.org/10.1103/physrevlett.131.053401

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