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Krylov complexity (K-complexity) and Arnoldi coefficients reveal diverse quantum localization phenomena in the quantum kicked rotor. These measures distinguish localization types and even detect chaos onset in localized quantum dynamics.

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Area of Science:

  • Quantum physics
  • Quantum chaos
  • Condensed matter physics

Background:

  • Krylov complexity (K-complexity) measures quantum state complexity and operator growth.
  • Quantum chaos is a key area of study in quantum mechanics.
  • The quantum kicked rotor (QKR) is a model system for exploring quantum chaos and localization.

Purpose of the Study:

  • Investigate diverse localization phenomena in the quantum kicked rotor (QKR).
  • Utilize K-complexity and Arnoldi coefficients to analyze quantum state complexity and operator growth.
  • Distinguish between different types of localization and detect the onset of chaos.

Main Methods:

  • Applying K-complexity analysis to quantum systems.
  • Utilizing Arnoldi coefficients to study operator dynamics.
  • Analyzing wave-function evolution on a Krylov chain.
  • Investigating four distinct localization scenarios in the QKR model.

Main Results:

  • K-complexity and Arnoldi coefficients exhibit distinct signatures for different localization scenarios.
  • The long-time behavior of K-complexity and wave-function evolution can differentiate localization types.
  • K-complexity captures both the degree and nature of localization.
  • Time-averaged K-complexity and Arnoldi coefficient scaling distinguish classical and quantum localization effects.
  • Arnoldi coefficients reveal chaos onset even in localized quantum dynamics.

Conclusions:

  • K-complexity and Arnoldi coefficients are powerful tools for characterizing quantum localization and chaos.
  • These measures provide insights into the fundamental mechanisms driving localization in quantum systems.
  • The study advances the understanding of quantum dynamics in complex systems like the QKR.