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Related Experiment Video

Updated: Apr 3, 2026

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
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Hyperdiffusion of quantum waves in random photonic lattices.

Alexander Iomin1

  • 1Department of Physics, Technion, Haifa, 32000, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 19, 2015
PubMed
Summary

This study analyzes hyperfast quantum wave packet diffusion in random optical lattices. We show mean-squared displacement spreads as a power law, dependent on the medium's random potential properties.

Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Photonics

Background:

  • Experimental studies show hyperdiffusive spreading of wave packets in random photonic lattices.
  • Understanding anomalous diffusion in disordered systems is crucial.

Purpose of the Study:

  • To perform a quantum-mechanical analysis of hyperfast diffusion in random optical lattices.
  • To theoretically explain the observed hyperdiffusive spreading of quantum wave packets.

Main Methods:

  • Rigorous quantum-mechanical calculation of the mean probability amplitude.
  • Analysis of the power-law spreading of the mean-squared displacement (MSD).

Main Results:

  • The MSD of a quantum wave packet spreads as a power law: 〈x2(t)〉∼tα, with 2<α≤3.

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  • The transport exponent α depends on the correlation properties of the random potential.
  • Turbulent diffusion (MSD ∼t3) is observed for time-δ-correlated potentials.
  • Hyperdiffusion with α=12/5 is found for arbitrary correlations.

    • Conclusions:

    • The theoretical framework explains hyperfast wave packet diffusion in disordered optical lattices.
    • The correlation properties of the random potential dictate the diffusion exponent.
    • This work provides a quantum-mechanical basis for understanding anomalous transport phenomena.