Numerical integration of the extended variable generalized Langevin equation with a positive Prony representable...

Area of Science:

• Computational physics and chemistry
• Soft matter physics
• Statistical mechanics

Background:

• Generalized Langevin Dynamics (GLD) models systems with memory effects, such as viscoelastic fluids and anomalous diffusion.
• Molecular Dynamics (MD) simulations incorporating GLD require efficient and stable numerical integrators.
• Existing methods face challenges with stability, convergence, and computational cost, especially with Prony series memory kernels.

Purpose of the Study:

• To derive and implement a novel family of extended variable integrators for the Generalized Langevin equation.
• To ensure numerical efficiency, stability, and known convergence properties for GLD simulations.
• To provide a convolution-free algorithm for LAMMPS MD software, reducing memory requirements.

Main Methods:

• Derivation of extended variable integrators for GLD with a positive Prony series memory kernel.
• Stability and error analysis to optimize integrator parameters.
• Implementation of the numerical algorithm within the LAMMPS molecular dynamics software package.
• Convolution-free formalism to avoid explicit storage of velocity time histories.

Main Results:

• A superlative choice of parameters was identified through stability and error analysis.
• The algorithm demonstrates exact conservation of first and second velocity moments in specific cases.
• Stable performance is observed in the limit of conventional Langevin dynamics.
• The convolution-free approach significantly reduces computational overhead.

Conclusions:

• The developed integrators offer an efficient, stable, and accurate method for simulating GLD in MD.
• The algorithm successfully handles complex systems, including those with harmonic potentials mapped to memory kernels.
• This work provides a valuable tool for researchers studying viscoelasticity, anomalous diffusion, and related phenomena.