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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Chaos and quantum scars in a coupled top model.

Debabrata Mondal1, Sudip Sinha1, S Sinha1

  • 1Indian Institute of Science Education and Research-Kolkata, Mohanpur, Nadia 741246, India.

Physical Review. E
|September 18, 2020
PubMed
Summary

This study explores a coupled top model, revealing quantum phase transitions and identifying quantum scars. These scars exhibit unique dynamics distinct from ergodic behavior, offering new insights into quantum systems.

Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Complex systems

Background:

  • The coupled top model describes interacting large spins.
  • Such models can exhibit complex phenomena including quantum phase transitions (QPTs).
  • Understanding the interplay between classical and quantum dynamics is crucial.

Purpose of the Study:

  • To investigate the semiclassical and quantum mechanical behavior of a coupled top model.
  • To identify and characterize phenomena like QPTs, dynamical transitions, and excited-state QPTs.
  • To explore the nature of quantum scars and their deviation from ergodic predictions.

Main Methods:

  • Semiclassical and quantum mechanical analysis of the coupled top model.
  • Examination of classical dynamics and entanglement entropy.

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  • Analysis of level spacing distributions and statistical properties of quantum states.
  • Investigation of unequal time commutators and survival probability.

    • Main Results:

    • The model exhibits QPTs, dynamical transitions, and excited-state QPTs.
    • Ergodic behavior is observed in classical dynamics and entanglement entropy above QPT.
    • Quantum scars are identified, showing dynamics that deviate from random matrix theory predictions.
    • Oscillatory behavior in dynamical quantities serves as a signature for quantum scars.

    Conclusions:

    • The coupled top model displays rich quantum and classical phenomena.
    • Quantum scars represent a deviation from universal ergodic behavior in interacting systems.
    • The identified dynamical signatures of quantum scars are crucial for their experimental detection.