论文标题
远程相互作用系统中的古典金石模式
Classical Goldstone modes in Long-Range Interacting Systems
论文作者
论文摘要
对于具有远距离相互作用的经典系统，每当固定状态自发打破哈密顿量的连续对称性时，就会存在软模式。除此之外，如果与对称性断裂相关的相应坐标是周期性的，则不同固定状态的相同能量和有限的$ n $热波动会导致质量中心的超延伸运动对总零动量的超延伸运动，这趋向于很长的时间进行正常的扩散。作为此示例，我们提供了二维自我磨化系统，一个自由电子激光器和汉密尔顿平均场（HMF）模型。对于后者，给出了质量中心运动的详细理论。我们还讨论了软模式与单个颗粒的平均场运动的耦合如何导致有限粒子数的强烈混沌行为，如HMF模型所示。
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.
