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Multifractality of open quantum systems.

Agustín M Bilen1, Ignacio García-Mata1, Bertrand Georgeot2

  • 1Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, CONICET, 7600 Mar del Plata, Argentina.

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This summary is machine-generated.

We found that quantum states in open systems with pseudointegrable classical dynamics exhibit multifractality, deviating from ergodicity. This multifractal behavior is linked to classical structures and observable in resonance states.

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Area of Science:

  • Quantum chaos
  • Statistical mechanics
  • Complex systems

Background:

  • Studying eigenstates of open quantum maps with pseudointegrable classical dynamics.
  • Closed quantum systems exhibiting multifractal properties.

Purpose of the Study:

  • To adapt existing frameworks for open chaotic quantum maps.
  • To establish the relationship between eigenstates and classical structures.
  • To quantify multifractality at various scales.

Main Methods:

  • General framework for open chaotic quantum maps.
  • Analysis of pseudointegrable classical dynamics.
  • Quantification of multifractality across scales.

Main Results:

  • Conjectured distribution of quantum states according to a hierarchy of classical structures.
  • Identified multifractality instead of ergodicity at each hierarchical level.
  • Observed multifractal behavior in long-lived resonance states at smaller scales.

Conclusions:

  • Quantum states in these open systems are multifractal, not ergodic.
  • Multifractality is linked to underlying classical structures.
  • Results provide guidance for experimental observation of multifractality in open systems.