Time domain approach to semiclassical dynamics: Breaking the log time barrier

Area of Science:

• Quantum mechanics
• Classical dynamics
• Chaos theory

Background:

• Semiclassical approximations are crucial for bridging quantum and classical mechanics.
• Chaos in classical dynamics was previously thought to limit the accuracy of semiclassical methods over time.
• Understanding the behavior of chaotic systems is essential in various scientific fields.

Purpose of the Study:

• To investigate the impact of classical chaos on semiclassical approximations in the time domain.
• To develop and demonstrate a method for calculating semiclassical propagation in nonlinear and chaotic systems.
• To assess the accuracy and timescale of these approximations for chaotic dynamics.

Main Methods:

• Developed a novel method for semiclassical propagation of initial states and correlation functions.
• Applied the method to nonlinear and chaotic dynamical systems.
• Analyzed the accuracy and breakdown timescale of the semiclassical approximations.

Main Results:

• The presence of chaos does not necessarily destroy semiclassical approximations.
• The proposed method demonstrates excellent accuracy for rather long times in chaotic systems.
• The timescale for the breakdown of accuracy is significantly longer than previously anticipated ('log time').

Conclusions:

• Semiclassical approximations remain viable and accurate for chaotic dynamics.
• The developed method provides a robust tool for studying quantum-classical correspondence in chaotic systems.
• This work extends the applicability of semiclassical methods to a broader range of complex dynamical systems.