Gupta Shamik, Mukamel David
Laboratoire de Physique Théorique et Modèles Statistiques, UMR 8626, Université Paris-Sud 11 and CNRS, Bâtiment 100, Orsay F-91405, France.
Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):052137. doi: 10.1103/PhysRevE.88.052137. Epub 2013 Nov 26.
We consider a long-range interacting system of N particles moving on a spherical surface under an attractive Heisenberg-like interaction of infinite range and evolving under deterministic Hamilton dynamics. The system may also be viewed as one of globally coupled Heisenberg spins. In equilibrium, the system has a continuous phase transition from a low-energy magnetized phase, in which the particles are clustered on the spherical surface, to a high-energy homogeneous phase. The dynamical behavior of the model is studied analytically by analyzing the Vlasov equation for the evolution of the single-particle distribution and numerically by direct simulations. The model is found to exhibit long-lived nonmagnetized quasistationary states (QSSs) which in the thermodynamic limit are dynamically stable within an energy range where the equilibrium state is magnetized. For finite N, these states relax to equilibrium over a time that increases algebraically with N. In the dynamically unstable regime, nonmagnetized states relax fast to equilibrium over a time that scales as lnN. These features are retained in presence of a global anisotropy in the magnetization.
我们考虑一个由N个粒子组成的长程相互作用系统，这些粒子在具有无限范围的吸引性类海森堡相互作用下在球面上运动，并在确定性哈密顿动力学下演化。该系统也可被视为全局耦合海森堡自旋系统之一。在平衡状态下，系统存在从低能磁化相到高能均匀相的连续相变，在低能磁化相中粒子聚集在球面上。通过分析单粒子分布演化的弗拉索夫方程对模型的动力学行为进行解析研究，并通过直接模拟进行数值研究。发现该模型表现出长寿命的非磁化准稳态（QSSs），在热力学极限下，这些态在平衡态被磁化的能量范围内是动态稳定的。对于有限的N，这些态在与N代数增长的时间内弛豫到平衡。在动态不稳定区域，非磁化态在与lnN成比例的时间内快速弛豫到平衡。在存在磁化全局各向异性的情况下，这些特征得以保留。
