Quantum-classical correspondence in the vicinity of periodic orbits

Area of Science:

• Quantum mechanics
• Classical mechanics
• Chaos theory

Background:

• Quantum-classical correspondence is a fundamental problem in physics, particularly in chaotic systems.
• Bohr's correspondence principle historically guided the transition from quantum to classical physics.
• Floquet systems offer a platform to study dynamical phenomena in periodically driven quantum systems.

Purpose of the Study:

• To develop a quantitative method for assessing Bohr's correspondence principle in chaotic systems.
• To determine the quantum number regimes where quantum-classical correspondence is observable near periodic orbits.
• To investigate the influence of classical periodic orbit stability on quantum dynamics.

Main Methods:

• Quantifying Bohr's correspondence principle using a novel method.
• Calculating quantum number ranges for observable correspondence.
• Analyzing the quantum kicked top (QKT) model, a paradigmatic chaotic system.
• Connecting classical bifurcations to quantum signatures.

Main Results:

• The method successfully quantifies quantum-classical correspondence near periodic orbits in Floquet systems.
• Classical periodic orbit stability is shown to directly impact quantum dynamics.
• Signatures of classical bifurcations were identified in the deep quantum regime of the QKT.
• The developed conditions explain the breakdown of quantum-classical correspondence in chaos.

Conclusions:

• The proposed method provides a robust tool for understanding quantum-classical correspondence in chaotic systems.
• It offers insights into the transition from quantum to classical behavior by analyzing periodic orbits.
• The findings have implications for explaining and predicting the limits of quantum-classical correspondence.