Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics

Area of Science:

• Quantum dynamics
• Statistical mechanics
• Theoretical chemistry

Background:

• Reduced density matrix dynamics are crucial for understanding open quantum systems.
• Existing methods like Nakajima-Zwanzig and Mori theory have limitations in nonequilibrium scenarios.
• Quasi-classical methods offer computational advantages but often lack accuracy.

Purpose of the Study:

• To present a unified theoretical framework combining Nakajima-Zwanzig and Mori theories.
• To develop a self-consistent equation for the memory kernel in nonequilibrium dynamics.
• To improve the accuracy of quasi-classical dynamics for open quantum systems.

Main Methods:

• A Dyson-type expansion is employed to derive the self-consistent memory kernel equation.
• The spin-boson model is used as a test case.
• Quasi-classical dynamics (Ehrenfest method) are utilized for auxiliary kernel calculations.
• Analysis of different projection operators (thermal and population-based) and auxiliary kernel closures.

Main Results:

• A novel formalism explicitly unifying Nakajima-Zwanzig and Mori theories is presented.
• A self-consistent equation for the memory kernel is derived, requiring only auxiliary kernels.
• Detailed analysis of memory kernel properties based on projection operators and auxiliary kernel closures.
• Demonstration of significant improvements over standard semi- and quasi-classical dynamics.

Conclusions:

• The developed formalism offers a versatile and accurate approach to nonequilibrium dynamics.
• The method provides a pathway to improved predictions for open quantum systems.
• Understanding memory kernel properties aids in selecting appropriate parameter spaces and computational strategies.