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Self-consistent inhomogeneous steady states in Hamiltonian mean-field dynamics
Pierre de Buyl1, David Mukamel, Stefano Ruffo
1Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2012
Summary
Researchers identified exact inhomogeneous steady states in long-range interacting systems. This method reveals relaxation times that diverge with system size, offering insights into Vlasov equation dynamics.
Area of Science:
- Statistical Physics
- Plasma Physics
- Dynamical Systems
Background:
- Long-lived quasistationary states are observed in systems with long-range interactions.
- These states are linked to stable solutions of the Vlasov equation.
- Previous studies on the Hamiltonian mean-field (HMF) model showed relaxation time divergence.
Purpose of the Study:
- To propose a method for identifying exact inhomogeneous steady states in the thermodynamic limit.
- To analyze the relaxation time of these states in the HMF model.
- To evaluate the stability limit of homogeneous steady states.
Main Methods:
- Analyzing models of uncoupled particles in an external field.
- Numerical simulations of the Hamiltonian mean-field (HMF) model.
- Investigating steady-state properties and relaxation times.
Main Results:
- A method for identifying exact inhomogeneous steady states was proposed.
- For the HMF model, relaxation time was found to diverge with N with an exponent γ ≈ 1.
- The method accurately determined the stability limit of homogeneous steady states.
Conclusions:
- The proposed method provides a way to find exact inhomogeneous steady states in systems with long-range interactions.
- The identified steady states exhibit relaxation times that diverge with system size.
- This approach is applicable to other globally coupled systems and aids in understanding initial condition-final state correspondence.
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