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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.