Quantization of classical maps with tunable Ruelle-Pollicott resonances

Area of Science:

• Quantum mechanics
• Classical dynamics
• Statistical physics

Background:

• Classical systems exhibit correlation decay governed by Ruelle-Pollicott resonances.
• Understanding the quantum-classical correspondence is a fundamental challenge in physics.

Purpose of the Study:

• To investigate the relationship between Ruelle-Pollicott resonances in classical systems and the properties of their quantum counterparts.
• To explore the role of these resonances in quantum energy eigenstate localization.

Main Methods:

• Construction of classical dynamical systems with controllable Ruelle-Pollicott resonances.
• Development of corresponding quantum systems to study resonance effects.
• Analysis of quantum energy eigenstate localization in relation to classical resonances.

Main Results:

• Established a direct link between classical correlation decay (Ruelle-Pollicott resonances) and quantum system behavior.
• Demonstrated that Ruelle-Pollicott resonances significantly influence the localization properties of quantum energy eigenstates.
• Showcased the utility of tunable resonances for probing quantum-classical connections.

Conclusions:

• Ruelle-Pollicott resonances provide a crucial bridge between classical dynamics and quantum localization phenomena.
• The study offers a novel framework for understanding quantum-classical correspondence through resonance analysis.
• Tunable resonances are a powerful tool for investigating complex quantum behaviors.