Improved configuration space sampling: Langevin dynamics with alternative mobility

Area of Science:

• Computational Physics
• Statistical Mechanics
• Materials Science

Background:

• Determining optimal configurations for large interacting particle systems is computationally challenging.
• Standard methods often struggle with convergence and exploring complex energy landscapes.

Purpose of the Study:

• To develop a novel and efficient method for finding optimal configurations of numerous interacting particles.
• To enhance the dynamics and convergence of systems described by Langevin equations.

Main Methods:

• Utilized a coarse-grained stochastic Langevin equation in the overdamped limit.
• Replaced standard mobility with an effective space-dependent inverse Hessian correlation matrix.
• Employed the Broyden-Fletcher-Goldfarb-Shannon method for updating the local mobility matrix.

Main Results:

• The new method demonstrates accelerated dynamics and improved convergence on convex potential energy surfaces.
• Stochastic noise facilitates access to transition states in concave regions.
• Quantitative analysis in 1D and 2D systems confirms higher efficiency compared to constant friction methods.
• Effective mobility dynamically adjusts friction based on configuration optimality.

Conclusions:

• The proposed method offers a significant efficiency improvement for optimizing large interacting particle systems.
• Adaptive friction based on Hessian correlations enhances exploration of potential energy landscapes.
• This approach provides a powerful tool for simulations in statistical mechanics and computational materials science.