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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.
Physical Review. E
|October 24, 2019
Summary
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.
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.
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