Bohmian trajectory from the "classical" Schrödinger equation.

Area of Science:

• Quantum mechanics
• Classical mechanics
• Dynamical systems theory

Background:

• Understanding the transition from quantum to classical behavior is a fundamental challenge.
• Periodically driven systems offer a rich platform for exploring complex dynamics, including chaos.
• The quartic oscillator is a standard model for studying nonlinear dynamics and quantum chaos.

Purpose of the Study:

• To investigate the quantum-classical correspondence in a periodically driven quartic oscillator.
• To analyze the role of Bohmian mechanics in bridging quantum and classical descriptions.
• To characterize the emergence of chaotic dynamics and its quantum manifestations.

Main Methods:

• Solving the time-dependent Schrödinger equation to obtain Bohmian trajectories.
• Computing phase plots to visualize system dynamics.
• Calculating the Kolmogorov-Sinai entropy for quantifying chaos.
• Comparing Bohmian trajectories with classical trajectories and quantum mechanical predictions.

Main Results:

• Bohmian trajectories at the classical limit exhibit behavior analogous to dissipative systems.
• Integrable and chaotic dynamics are observed in the driven quartic oscillator.
• The Kolmogorov-Sinai entropy provides a quantitative measure of chaos in both classical and Bohmian descriptions.
• Discrepancies and similarities between classical, Bohmian, and quantum dynamics are identified.

Conclusions:

• Bohmian mechanics offers a valuable framework for studying quantum-classical correspondence.
• The classical limit of quantum mechanics can exhibit non-intuitive behaviors, such as mimicking dissipation.
• The study provides insights into the quantum origins of classical chaos in driven nonlinear systems.