Probing the localization effects in Krylov basis

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.