Barrier-induced chaos in a kicked rotor: Classical subdiffusion and quantum localization

Area of Science:

• Physics
• Quantum Mechanics
• Chaos Theory

Background:

• Classical dynamics and quantum localization are typically studied under Kolmogorov-Arnold-Moser (KAM) theorem assumptions.
• Systems violating KAM theorem assumptions present unique challenges in understanding their dynamics.

Purpose of the Study:

• To investigate the relationship between classical chaos and quantum localization in a system that breaks KAM theorem conditions.
• To analyze the impact of a discontinuous potential barrier on chaotic dynamics and energy growth regimes.
• To understand how non-KAM classical dynamics influence quantum localization and quantum break time.

Main Methods:

• Studied a kicked rotor model with a discontinuous potential barrier.
• Analyzed the emergence of multiple subdiffusive energy growth regimes in the classical system.
• Investigated the quantized version of the system to observe dynamical localization.
• Examined the dependence of quantum break time on subdiffusion exponents.

Main Results:

• The discontinuous barrier induces chaos and more than two distinct subdiffusive energy growth regimes, an unusual feature for Hamiltonian chaos.
• Dynamical localization in the quantized system shows a clear imprint of non-KAM classical dynamics.
• Quantum break time is dependent on the subdiffusion exponents derived from the classical dynamics.

Conclusions:

• The study demonstrates a direct link between non-KAM classical dynamics and quantum localization.
• The observed subdiffusive regimes and their influence on quantum break time offer new insights into chaotic quantum systems.
• The proposed system is potentially feasible for experimental realization.