de Buyl Pierre, Mukamel David, Ruffo Stefano
Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Dec;84(6 Pt 1):061151. doi: 10.1103/PhysRevE.84.061151. Epub 2011 Dec 28.
Long-lived quasistationary states, associated with stationary stable solutions of the Vlasov equation, are found in systems with long-range interactions. Studies of the relaxation time in a model of N globally coupled particles moving on a ring, the Hamiltonian mean-field model (HMF), have shown that it diverges as N(γ) for large N, with γ1.7 for some initial conditions with homogeneously distributed particles. We propose a method for identifying exact inhomogeneous steady states in the thermodynamic limit, based on analyzing models of uncoupled particles moving in an external field. For the HMF model, we show numerically that the relaxation time of these states diverges with N with the exponent γ ~/= 1. The method, applicable to other models with globally coupled particles, also allows an exact evaluation of the stability limit of homogeneous steady states. In some cases, it provides a good approximation for the correspondence between the initial condition and the final steady state.
在具有长程相互作用的系统中发现了与弗拉索夫方程的稳态稳定解相关的长寿命准稳态。对在环上运动的(N)个全局耦合粒子模型（哈密顿平均场模型，HMF）中的弛豫时间的研究表明，对于大(N)，它以(N^{\gamma})的形式发散，对于粒子均匀分布的某些初始条件，(\gamma\gt1.7)。我们提出了一种基于分析在外场中运动的非耦合粒子模型来识别热力学极限下精确非均匀稳态的方法。对于HMF模型，我们通过数值表明这些状态的弛豫时间以(N)的幂次发散，指数(\gamma\neq1)。该方法适用于其他具有全局耦合粒子的模型，还允许精确评估均匀稳态的稳定性极限。在某些情况下，它为初始条件和最终稳态之间的对应关系提供了一个很好的近似。
