Generalized Langevin dynamics simulation with non-stationary memory kernels: How to make noise

Area of Science:

• Computational physics
• Statistical mechanics
• Non-equilibrium systems

Background:

• Generalized Langevin Equation (GLE) describes complex dynamics.
• Non-stationary memory kernels arise in coarse-grained time-dependent systems.
• Projection operator formalism is used for coarse-graining.

Purpose of the Study:

• To present a numerical method for simulating stochastic dynamics with non-stationary memory kernels.
• To enable the simulation of coarse-grained models for driven processes.
• To reproduce observable distributions up to a given moment order.

Main Methods:

• Developing a numerical method for GLE with non-stationary memory.
• Replacing deterministic fluctuating forces with stochastic processes.
• Extracting memory kernels from microscopic simulation data.

Main Results:

• The proposed method accurately reproduces observable distributions.
• It allows for the simulation of stochastic dynamics in driven systems.
• The method is compatible with extracting memory kernels from underlying models.

Conclusions:

• A novel numerical method for simulating complex stochastic dynamics is introduced.
• This method facilitates the study of coarse-grained models for driven processes.
• The approach provides a way to bridge microscopic and coarse-grained descriptions.