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Stochastic processes with finite correlation time: modeling and application to the generalized Langevin equation
1Institute of Nuclear Physics, PL-31-342 Kraków, Poland.
Summary
The kangaroo process (KP) models random noise with different covariances. A modified KP avoids issues with the fluctuation-dissipation theorem, making it suitable for physical applications.
Area of Science:
- Statistical Physics
- Stochastic Processes
Background:
- The kangaroo process (KP) exhibits diverse covariance properties, making it a potential model for random noise.
- Understanding noise characteristics is crucial in various scientific disciplines, including physics.
Purpose of the Study:
- To explore the properties of the kangaroo process (KP) with exponential, stretched exponential, and algebraic (power-law) covariances.
- To apply the KP as a noise model in the generalized Langevin equation (GLE) and investigate its compatibility with the fluctuation-dissipation theorem (FDT).
- To develop a modified KP model that resolves FDT inconsistencies for physical applications.
Main Methods:
- Analysis of KP properties for different covariance functions.
- Monte Carlo simulations to solve the generalized Langevin equation with KP noise.
- Comparison of simulation results with the fluctuation-dissipation theorem.
Main Results:
- The kangaroo process exhibits distinct behaviors for exponential, stretched exponential, and power-law covariances.
- Direct application of KP in the GLE can lead to violations of the fluctuation-dissipation theorem due to changes in probability distributions.
- A modified kangaroo process was developed that adheres to the fluctuation-dissipation theorem.
Conclusions:
- The kangaroo process is a versatile model for various types of noise.
- Standard KP in GLE can violate the fluctuation-dissipation theorem.
- A modified KP offers a noise model consistent with physical principles for the generalized Langevin equation.
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