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Effective mass approach to memory in non-Markovian systems
M Wiśniewski1, J Łuczka1, J Spiechowicz1
1Institute of Physics, University of Silesia, 41-500 Chorzów, Poland.
Physical Review. E
|May 17, 2024
Summary
This study simplifies non-Markovian dynamics by using an effective mass in a memoryless Langevin equation. This approach accurately captures memory effects, aiding the study of complex systems.
Area of Science:
- Physics
- Statistical Mechanics
- Complex Systems
Background:
- Non-Markovian dynamics, crucial for understanding systems with memory, are often simplified using the Markovian approximation, neglecting memory effects.
- Pioneering experiments in areas like active matter highlight the incomplete theoretical understanding of non-Markovian phenomena.
- Studying memory effects is vital for advancing theoretical models in physics.
Purpose of the Study:
- To develop a method for studying memory effects in non-Markovian systems.
- To approximate a non-Markovian system with a memoryless Langevin equation.
- To lay the foundation for analyzing memory-related corrections to Markovian dynamics.
Main Methods:
- Describing a non-Markovian system using the Generalized Langevin Equation (GLE) for a Brownian particle.
- Approximating the non-Markovian system with a memoryless Langevin equation.
- Reproducing memory effects through an effective mass (M*) dependent on the memory kernel.
Main Results:
- Demonstrated that memory effects in a non-Markovian system can be accurately represented by an effective mass in a memoryless Langevin equation.
- The effective mass (M*) is solely determined by the memory kernel's form.
- Established a method to study memory-related corrections to Markovian dynamics.
Conclusions:
- The proposed method provides a valuable tool for analyzing non-Markovian dynamics.
- This approach simplifies the study of memory effects in complex systems.
- The findings pave the way for deeper insights into phenomena currently limited by the Markovian approximation.
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