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

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.