Semiclassical dynamics in Wigner phase space I: Adiabatic hybrid Wigner dynamics

Area of Science:

• Quantum Mechanics
• Chemical Physics
• Computational Chemistry

Background:

• The Wigner phase space formulation offers a powerful framework for quantum dynamics, linking quantum and classical mechanics.
• Existing semiclassical (SC) methods face challenges in accurately describing complex system-bath interactions and quantum interference effects.

Purpose of the Study:

• To derive and validate a novel hybrid semiclassical method for quantum dynamic calculations in Wigner phase space.
• To improve the accuracy and efficiency of semiclassical methods for adiabatic processes, particularly in system-bath scenarios.

Main Methods:

• Derivation of the double Herman-Kluk (DHK) and linearized SC (LSC) approximations in Wigner phase space.
• Development and application of the Adiabatic Hybrid Wigner Dynamics (AHWD) method, combining DHK and LSC treatments for different degrees of freedom.
• Utilizing stationary phase approximation to connect DHK and LSC methods.

Main Results:

• AHWD accurately captures quantum interference effects in coupled oscillator models.
• The method effectively describes the decoherence of vibrational probability density for a model I2 Morse oscillator coupled to a thermal bath.
• AHWD significantly mitigates the sign problem inherent in quantum dynamic calculations.
• Reduced dimensional prefactors enable tractable calculations for complex system-bath problems.

Conclusions:

• The proposed AHWD method represents a significant advancement in semiclassical dynamics for adiabatic quantum systems.
• AHWD offers a computationally efficient and accurate approach to studying quantum phenomena in complex molecular systems.
• This work lays the foundation for extending hybrid semiclassical dynamics to non-adiabatic processes in subsequent research.