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Ubiquitous quantum scarring does not prevent ergodicity
Saúl Pilatowsky-Cameo1, David Villaseñor1, Miguel A Bastarrachea-Magnani2,3
1Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico.
Nature Communications
|February 9, 2021
Summary
Most quantum states in chaotic systems are not ergodic as expected. Instead, all eigenstates in the chaotic Dicke model exhibit quantum scarring, challenging the assumption of uniform phase space distribution.
Area of Science:
- Quantum chaos
- Statistical mechanics
- Quantum information theory
Background:
- Ergodicity in classical systems implies uniform phase space exploration.
- Quantum mechanics, via Born's rules, suggests uniform distribution of quantum states in chaotic regimes.
- Quantum scarring, the localization of eigenstates along unstable periodic orbits, contradicts this simplified view.
Purpose of the Study:
- To investigate the distribution of quantum states in the chaotic Dicke model.
- To determine if eigenstates in this model are ergodic or exhibit scarring.
- To re-evaluate the concept of quantum ergodicity in interacting quantum systems.
Main Methods:
- Analysis of eigenstates in the chaotic Dicke model.
- Examination of phase space distribution of quantum states.
- Comparison with classical ergodicity and quantum scarring phenomena.
Main Results:
- All eigenstates of the chaotic Dicke model demonstrate quantum scarring.
- Even highly delocalized states occupy at most half of the available phase space.
- Uniform quantum ergodicity is only observed as an ensemble average over time.
Conclusions:
- The assumption of widespread quantum ergodicity in chaotic models is challenged.
- Quantum scarring is a prevalent feature in the chaotic Dicke model.
- Ergodicity in this quantum system is an emergent property of temporal averages, not a property of individual eigenstates.
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