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Linear response theory for long-range interacting systems in quasistationary states
Aurelio Patelli1, Shamik Gupta, Cesare Nardini
1Dipartimento di Fisica ed Astronomia, Università di Firenze and INFN, Via Sansone 1, IT-50019 Sesto Fiorentino, Italy.
Summary
Long-range interacting systems in quasistationary states (QSS) respond to external perturbations. This study derives a formula for this response, validated by simulations of the Hamiltonian mean-field model.
Area of Science:
- Statistical Mechanics
- Non-equilibrium Dynamics
- Complex Systems
Background:
- Long-range interacting systems exhibit long-lived quasistationary states (QSS) with lifetimes dependent on system size.
- Understanding the behavior of these systems under external influence is crucial for non-equilibrium statistical mechanics.
Purpose of the Study:
- To investigate the response of a long-range system in a QSS to external perturbations.
- To develop a theoretical framework for predicting this response.
Main Methods:
- Analysis of the Vlasov equation for the single-particle phase-space distribution.
- Linearization of the perturbed Vlasov equation around a QSS.
- Application to the Hamiltonian mean-field model.
Main Results:
- Derivation of a formal expression for the response to small perturbations.
- Obtained an explicit response formula for coordinate-homogeneous QSS.
- Predictions for three QSSs in the Hamiltonian mean-field model showed good agreement with N-particle simulations.
Conclusions:
- The theoretical framework accurately predicts the response of QSSs to perturbations.
- Demonstrated long-time relaxation of a water-bag QSS to equilibrium.
- Highlights the importance of QSS dynamics in long-range interacting systems.
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