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This study introduces a new method to analyze heavy-tailed systems where standard large-deviations principles fail. The research reveals a bifractal nature in spreading particle packets, offering insights into rare events.

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Area of Science:

  • Statistical Physics
  • Quantum Optics
  • Non-equilibrium Systems

Background:

  • Standard large-deviations theory applies to thin-tailed systems, describing exponential falloff.
  • Heavy-tailed systems exhibit fat tails at intermediate scales, deviating from standard theory.
  • Understanding rare events in these systems is crucial for statistical properties.

Purpose of the Study:

  • To develop a new approach for studying large fluctuations in heavy-tailed systems.
  • To investigate the spatial density of laser-cooled atoms, which display fat-tailed behavior.
  • To analyze rare events beyond intermediate scales that dominate system properties.

Main Methods:

  • Utilized a novel friction mechanism induced by laser fields.
  • Employed the recently proposed non-normalized infinite-covariant density approach.
  • Investigated the spatial density P_{t}(x) of laser-cooled atoms.

Main Results:

  • The spatial density of laser-cooled atoms shows fat tails at intermediate scales.
  • Rare events beyond these scales were analyzed, revealing their dominance.
  • A bifractal nature of the spreading packet was identified, arising from small and large fluctuations.
  • General relations were derived for systems with multifractal moments.

Conclusions:

  • The novel approach successfully analyzes heavy-tailed systems where standard methods fail.
  • The study reveals a bifractal nature in spreading packets due to a new friction mechanism.
  • The derived relations extend the theory to a broader class of multifractal systems.