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

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|August 18, 2023
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Summary
This summary is machine-generated.

We studied exciton propagation in lattices with power-law hopping and dephasing. In strong dephasing, dynamics become an exclusion process with long jumps, exhibiting anomalous diffusion and Lévy stable distributions.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Dynamics
  • Statistical Mechanics

Background:

  • Exciton dynamics are crucial for energy transport in various materials.
  • Dephasing significantly impacts quantum system evolution.
  • Power-law hopping introduces long-range interactions in lattice models.

Purpose of the Study:

  • Analyze exciton propagation in d-dimensional lattices with power-law hopping and dephasing.
  • Investigate the transition from quantum to classical dynamics under strong dephasing.
  • Characterize the anomalous diffusion and spatial distribution of excitons.

Main Methods:

  • Generalized Haken-Strobl-Reineker model for exciton-photon interaction.
  • Analysis in the strong dephasing (quantum Zeno) regime.
  • Analytical computation of spatial distribution and diffusion properties.
  • Investigation of many-exciton systems with domain-wall initial profiles.

Main Results:

  • In strong dephasing, exciton dynamics follow a classical master equation for an exclusion process with long jumps.
  • Anomalous diffusion is observed, with Lévy stable distributions for α ≤ αcr = (d+2)/2.
  • For α > αcr, a mixed Gaussian profile with algebraic tails emerges, showing coexistence of diffusion and Lévy flights.
  • Many-exciton systems exhibit algebraic tails, accelerating thermalization with longer hopping ranges.

Conclusions:

  • Strong dephasing transforms quantum exciton dynamics into classical long-jump exclusion processes.
  • The spatial distribution exhibits a critical transition and anomalous diffusion, including Lévy flights.
  • Results offer insights into energy transport and thermalization, relevant for cold atoms and molecular aggregates.