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Ubiquitous quantum scarring does not prevent ergodicity.

Saúl Pilatowsky-Cameo1, David Villaseñor1, Miguel A Bastarrachea-Magnani2,3

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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.

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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.