Characterizing the mixed eigenstates in kicked top model through the out-of-time-order correlator.

Area of Science:

• Quantum mechanics
• Complex systems
• Statistical physics

Background:

• Generic systems possess mixed classical phase space.
• Eigenstate properties in these systems are crucial for understanding quantum phenomena like thermalization and localization.
• Understanding mixed eigenstates is key to advancing quantum physics.

Purpose of the Study:

• To investigate the dynamical signatures of mixed eigenstates.
• To explore the utility of the out-of-time-order correlator (OTOC) for characterizing these eigenstates.
• To deepen the understanding of quantum complex systems.

Main Methods:

• Utilized the kicked top model, a standard model for studying quantum chaos.
• Employed the out-of-time-order correlator (OTOC) to probe system dynamics.
• Analyzed both short- and long-time behaviors of the OTOC.

Main Results:

• Demonstrated that different types of eigenstates exhibit distinct dynamical signatures in the OTOC.
• Showcased how the OTOC's time evolution reflects the nature of mixed eigenstates.
• Established a conjecture that OTOC dynamics can serve as an indicator for mixed eigenstates.

Conclusions:

• The out-of-time-order correlator (OTOC) is a valuable tool for studying quantum complex systems.
• The study provides new insights into the characteristics of mixed eigenstates.
• Findings confirm the OTOC's role in characterizing quantum dynamics and eigenstates.