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

• URL: http://arxiv.org/abs/2212.07744v2
• Date: Wed, 23 Aug 2023 13:33:40 GMT
• Title: Anomalous diffusion in the Long-Range Haken-Strobl-Reineker model
• Authors: Alberto Giuseppe Catalano and Francesco Mattiotti and J\'er\^ome Dubail and David Hagenm\"uller and Toma\v{z} Prosen and Fabio Franchini and Guido Pupillo
• Abstract summary: We show that in the strong dephasing regime the dynamics is described by a classical master equation for an exclusion process with long jumps. Our results are directly relevant to experiments with cold trapped ions, Rydberg atoms and supramolecular dye aggregates.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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