长程相互作用系统中的经典Goldstone模
Classical Goldstone modes in Long-Range Interacting Systems
摘要：
对于一个具有长程相互作用的经典系统，只要一个定态自发地破坏了哈密顿量的连续对称性，就存在一个软模。除此之外，如果与对称性破缺相关联的对应坐标是周期性的，则不同定态的相同能量和有限的$N$热涨落导致总动量为零的质心的超扩散运动，其在很长时间内趋向于正常扩散。作为例子，我们提供了一个二维自引力系统，一个自由电子激光和哈密顿平均场（HMF）模型。对于后者，给出了详细的质心运动理论。我们还讨论了如何耦合的软模式的平均场运动的单个粒子可能会导致强烈的混沌行为的有限的粒子数，如所示的HMF模型。
英文摘要：
For a classical system with long-range interactions, a soft mode exists whenever a stationary state spontaneously breaks a continuous symmetry of the Hamiltonian. Besides that, if the corresponding coordinate associated to the symmetry breaking is periodic, the same energy of the different stationary states and finite $N$ thermal fluctuations result in a superdiffusive motion of the center of mass for total zero momentum, that tends to a normal diffusion for very long-times. As examples of this, we provide a two-dimensional self-gravitating system, a free electron laser and the Hamiltonian Mean-Field (HMF) model. For the latter, a detailed theory for the motion of the center of mass is given. We also discuss how the coupling of the soft mode to the mean-field motion of individual particles may lead to strong chaotic behavior for a finite particle number, as illustrated by the HMF model.
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