Atenas Boris, Curilef Sergio
Departamento de Física, Universidad Católica del Norte, Avenida Angamos 0610, Antofagasta, Chile.
Phys Rev E. 2017 Feb;95(2-1):022110. doi: 10.1103/PhysRevE.95.022110. Epub 2017 Feb 8.
A Hamiltonian mean field model, where the potential is inspired by dipole-dipole interactions, is proposed to characterize the behavior of systems with long-range interactions. The dynamics of the system remains in quasistationary states before arriving at equilibrium. The equilibrium is analytically derived from the canonical ensemble and coincides with that obtained from molecular dynamics simulations (microcanonical ensemble) at only long time scales. The dynamics of the system is characterized by the behavior of the mean value of the kinetic energy. The significance of the results, compared to others in the recent literature, is that two plateaus sequentially emerge in the evolution of the model under the special considerations of the initial conditions and systems of finite size. The first plateau decays to a different second one before the system reaches equilibrium, but the dynamics of the system is expected to have only one plateau when the thermodynamics limit is reached because the difference between them tends to disappear as N tends to infinity. Hence, the first plateau is a type of quasistationary state the lifetime of which depends on a power law of N and the second seems to be a true quasistationary state as reported in the literature. We characterize the general behavior of the model according to its dynamics and thermodynamics.
提出了一种哈密顿平均场模型，其势受偶极 - 偶极相互作用启发，用于描述具有长程相互作用的系统的行为。系统的动力学在达到平衡之前保持在准稳态。平衡态通过正则系综解析得出，并且仅在长时间尺度上与分子动力学模拟（微正则系综）得到的结果一致。系统的动力学由动能平均值的行为来表征。与近期文献中的其他结果相比，该结果的重要意义在于，在初始条件和有限尺寸系统的特殊考虑下，模型演化过程中会依次出现两个平台期。在系统达到平衡之前，第一个平台期会衰减为另一个不同的第二个平台期，但当达到热力学极限时，系统的动力学预计只会有一个平台期，因为随着(N)趋于无穷大，它们之间的差异趋于消失。因此，第一个平台期是一种准稳态，其寿命取决于(N)的幂律，而第二个平台期似乎如文献报道的那样是真正的准稳态。我们根据模型的动力学和热力学来描述其一般行为。
