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Natural cutoff in Lévy flights caused by dissipative nonlinearity
Aleksei V Chechkin1, Vsevolod Yu Gonchar, Joseph Klafter
1Institute for Theoretical Physics NSC KIPT, Kharkov, Ukraine.
Summary
Lévy flight models, used for complex systems, face issues with particle dynamics. Nonlinear friction regularizes Lévy noise, creating a finite velocity variance and a natural cutoff in velocity distribution.
Area of Science:
- Physics
- Complex Systems
- Stochastic Processes
Background:
- Lévy flight models are frequently employed to model stochastic processes in complex systems.
- However, diverging position and velocity fluctuations in Lévy flights pose physical challenges for describing the dynamics of massive particles.
Purpose of the Study:
- To investigate the regularization of Lévy noise in random walker dynamics.
- To demonstrate how nonlinear friction can address the physical limitations of Lévy flight models.
Main Methods:
- Analysis of random walker dynamics subjected to Lévy noise.
- Introduction of nonlinear friction to the system.
Main Results:
- Nonlinear friction regularizes the velocity distribution of a random walker under Lévy noise.
- This regularization results in a natural cutoff in the velocity distribution.
- Finite velocity variance is achieved, resolving physical inconsistencies.
Conclusions:
- Nonlinear friction provides a physically consistent framework for Lévy flight dynamics.
- This approach overcomes the limitations of diverging fluctuations in complex systems.
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