A new trajectory branching approximation to propagate the mixed quantum-classical Liouville equation

Area of Science:

• Quantum dynamics simulations
• Theoretical chemistry
• Computational physics

Background:

• The mixed quantum-classical Liouville (MQCL) equation is a key tool for simulating quantum dynamics.
• The conventional mean field approximation in MQCL can become inaccurate under certain conditions.

Purpose of the Study:

• To develop a new trajectory branching method as an improvement over the standard mean field approximation.
• To address the limitations of the mean field approximation in mixed quantum-classical dynamics.

Main Methods:

• Derivation of a new trajectory branching method from the MQCL equation.
• Utilizing the mean field approximation for short-time propagation.
• Branching trajectories when the mean field description becomes invalid.
• Defining new variables to monitor deviations and deriving their equations of motion via first moment expansion.

Main Results:

• The new method successfully propagates mixed quantum-classical dynamics.
• It correctly addresses limitations of the mean field approximation in several test cases.
• Demonstrated accuracy on one-dimensional, two-surface problems.

Conclusions:

• The developed trajectory branching method offers a more accurate approach to mixed quantum-classical dynamics.
• This method provides a valuable alternative to the conventional mean field approximation.
• It enhances the reliability of simulations involving complex quantum-classical interactions.