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Perturbation spreading in many-particle systems: a random walk approach
V Zaburdaev1, S Denisov, P Hänggi
1School of Engineering and Applied Science, Harvard University, Cambridge, Massachusetts 02138, USA.
Physical Review Letters
|June 4, 2011
Summary
We show that localized perturbations in many-particle systems behave like a single particle in a fluctuating medium. This behavior is modeled using a continuous-time random walk, revealing connections between many-body dynamics and Lévy walk diffusion.
Area of Science:
- Statistical Mechanics
- Complex Systems
- Nonlinear Dynamics
Background:
- Investigating perturbation propagation in interacting many-particle systems is crucial for understanding complex phenomena.
- Many-body Hamiltonian dynamics present challenges in predicting emergent behavior.
Purpose of the Study:
- To model the propagation of localized perturbations in interacting many-particle systems.
- To establish a connection between many-body dynamics and single-particle random walk models.
Main Methods:
- Utilized a continuous-time random walk (CTRW) framework to model perturbation spread.
- Employed two archetype ergodic systems: a hard-point gas (two unequal masses) and a Fermi-Pasta-Ulam chain.
- Analyzed perturbation profiles and compared them with single-particle diffusion profiles.
Main Results:
- Perturbation propagation in many-body systems can be accurately captured by a single-particle random walk in a fluctuating medium.
- Demonstrated that perturbation profiles align with the diffusion profiles of the single-particle Lévy walk approach.
- Established elementary algebraic relationships between CTRW parameters and the physical parameters of the many-body systems.
Conclusions:
- The Lévy walk approach provides a powerful and simplified model for understanding perturbation dynamics in complex many-body systems.
- This work bridges the gap between microscopic Hamiltonian dynamics and macroscopic emergent behaviors like diffusion.
- The findings offer a new perspective on modeling transport phenomena in statistical mechanics.
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