Memory Corrections to Markovian Langevin Dynamics.

Area of Science:

• Physics
• Statistical Mechanics
• Non-Markovian Dynamics

Background:

• Analyzing non-Markovian systems and memory effects presents a significant challenge in physics.
• Brownian motion with correlated thermal fluctuations serves as a key model system.

Purpose of the Study:

• To derive a recently proposed approximation for non-Markovian Brownian dynamics within the Markovian embedding technique.
• To calculate memory corrections to the Markovian dynamics of a Brownian particle.

Main Methods:

• Utilizing the Markovian embedding technique to approximate non-Markovian dynamics.
• Representing the memory kernel using the Prony series.
• Calculating first- and second-order memory corrections.

Main Results:

• The approximation, which uses a memoryless model with an effective mass (M* < M), can be derived via Markovian embedding.
• The second-order correction further reduces the effective mass, increasing approximation precision.
• The method provides a framework for higher-order memory corrections.

Conclusions:

• The Markovian embedding technique offers a rigorous derivation for memory-induced phenomena in Brownian motion.
• This work advances the understanding and modeling of non-Markovian systems.
• The study paves the way for developing more accurate approximations in statistical physics.