Simple and efficient algorithms based on Volterra equations to compute memory kernels and projected cross-correlation...

Area of Science:

• Statistical Mechanics
• Computational Physics

Background:

• The Mori-Zwanzig formalism is a key tool for deriving generalized Langevin equations (GLEs) from microscopic dynamics.
• Calculating memory kernels and projected time correlation functions within this framework can be computationally intensive.

Purpose of the Study:

• To develop an efficient and convenient strategy for obtaining projected time correlation functions and memory kernel contributions for GLEs.
• To investigate the role of repulsive-attractive cross-contributions to memory effects in the self-diffusion of tagged particles.

Main Methods:

• Derivation of coupled Volterra equations from orthogonal dynamics of system variables.
• Application of standard numerical inversion methods to solve the obtained Volterra equations.
• Investigation of the memory kernel for tagged particle diffusion in a bulk Lennard-Jones fluid.

Main Results:

• A set of coupled Volterra equations was derived, relating projected time correlation functions.
• A computationally efficient strategy was established for calculating projected time correlation functions and memory kernel contributions.
• The repulsive-attractive cross-contribution to memory effects was found to be small but non-zero for self-diffusion.

Conclusions:

• The developed method provides a convenient and efficient approach for analyzing memory effects in complex systems.
• The study quantifies the contribution of specific interactions to the self-diffusion coefficient in a Lennard-Jones fluid.