Linear response theory for long-range interacting systems in quasistationary states

被引:21
|
作者
Patelli, Aurelio [1 ,2 ]
Gupta, Shamik [3 ]
Nardini, Cesare [1 ,2 ,3 ]
Ruffo, Stefano [3 ,4 ,5 ,6 ]
机构
[1] Univ Florence, Dipartimento Fis & Astron, IT-50019 Sesto Fiorentino, Italy
[2] Ist Nazl Fis Nucl, IT-50019 Sesto Fiorentino, Italy
[3] Univ Lyon, CNRS, Ecole Normale Super Lyon, Phys Lab, FR-69364 Lyon 07, France
[4] Univ Florence, Dipartimento Energet Sergio Stecco, CNISM, IT-50139 Florence, Italy
[5] Univ Florence, CSDC, CNISM, IT-50139 Florence, Italy
[6] Ist Nazl Fis Nucl, IT-50139 Florence, Italy
来源
PHYSICAL REVIEW E | 2012年 / 85卷 / 02期
关键词
STABILITY; DYNAMICS;
D O I
10.1103/PhysRevE.85.021133
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
Long-range interacting systems, while relaxing to equilibrium, often get trapped in long-lived quasistationary states which have lifetimes that diverge with the system size. In this work, we address the question of how a long-range system in a quasistationary state (QSS) responds to an external perturbation. We consider a long-range system that evolves under deterministic Hamilton dynamics. The perturbation is taken to couple to the canonical coordinates of the individual constituents. Our study is based on analyzing the Vlasov equation for the single-particle phase-space distribution. The QSS represents a stable stationary solution of the Vlasov equation in the absence of the external perturbation. In the presence of small perturbation, we linearize the perturbed Vlasov equation about the QSS to obtain a formal expression for the response observed in a single-particle dynamical quantity. For a QSS that is homogeneous in the coordinate, we obtain an explicit formula for the response. We apply our analysis to a paradigmatic model, the Hamiltonian mean-field model, which involves particles moving on a circle under Hamiltonian dynamics. Our prediction for the response of three representative QSSs in this model (the water-bag QSS, the Fermi-Dirac QSS, and the Gaussian QSS) is found to be in good agreement with N-particle simulations for large N. We also show the long-time relaxation of the water-bag QSS to the Boltzmann-Gibbs equilibrium state.
引用
收藏
页数:12
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