Approximate but accurate quantum dynamics from the Mori formalism. II. Equilibrium time correlation functions

Area of Science:

• Theoretical chemistry
• Quantum dynamics
• Condensed matter physics

Background:

• Calculating equilibrium time correlation functions for many-body quantum systems is a significant challenge.
• The Nakajima-Zwanzig-Mori formalism has shown success in nonequilibrium dynamics.

Purpose of the Study:

• To extend the Nakajima-Zwanzig-Mori formalism for symmetrized equilibrium time correlation functions.
• To apply the method to the spin-boson model.

Main Methods:

• Utilized a Dyson-type expansion of the projected propagator.
• Developed a self-consistent solution for the memory kernel.
• Employed the mean-field Ehrenfest method for demonstration.

Main Results:

• The extended formalism provides accurate and efficient calculations for the spin-boson model.
• Demonstrated significant improvements in accuracy and efficiency compared to bare Ehrenfest dynamics.
• Analyzed the impact of kernel closures and initial density operator accuracy.

Conclusions:

• The developed self-consistent formalism offers a powerful approach for computing equilibrium time correlation functions.
• This method provides a substantial advancement over existing techniques for quantum system dynamics.
• Further research can explore variations in kernel closures and initial conditions.