Rajak Atanu, Dana Itzhack
Department of Physics, Bar-Ilan University, Ramat Gan 5290002, Israel.
Presidency University, Kolkata, West Bengal 700073, India.
Phys Rev E. 2020 Dec;102(6-1):062120. doi: 10.1103/PhysRevE.102.062120.
We study stability and chaotic-transport features of paradigmatic nonequilibrium many-body systems, i.e., periodically kicked and interacting particles, for arbitrary number of particles, nonintegrability strength unbounded from above, and different interaction cases. We rigorously show that under the latter general conditions and in strong nonintegrability regimes there exist fully stable orbits, accelerator-mode (AM) fixed points, performing ballistic motion in momentum. These orbits exist despite of the completely and strongly chaotic phase space with generally fast Arnol'd diffusion. It is numerically shown that an "isolated chaotic zone" (ICZ), separated from the rest of the phase space, remains localized around an AM fixed point for long times even when this point is partially stable in only a few phase-space directions. This localization should reflect an Arnol'd diffusion in an ICZ much slower than that in the rest of phase space. The time evolution of the mean kinetic energy of an initial ensemble containing an ICZ exhibits superdiffusion instead of normal chaotic diffusion.
我们研究了典型非平衡多体系统的稳定性和混沌输运特性，即周期性驱动且相互作用的粒子，研究对象包括任意数量的粒子、非可积强度无上限以及不同的相互作用情形。我们严格证明，在上述一般条件下以及强非可积区域中，存在完全稳定的轨道、加速器模式（AM）不动点，其在动量空间中进行弹道运动。尽管相空间完全且强烈混沌，存在通常快速的阿诺德扩散，但这些轨道依然存在。数值结果表明，即使一个“孤立混沌区”（ICZ）在仅少数相空间方向上部分稳定，它与相空间其余部分分离，仍能长时间局域在一个AM不动点周围。这种局域化应反映出ICZ中的阿诺德扩散比相空间其余部分的扩散慢得多。包含ICZ的初始系综平均动能的时间演化表现出超扩散而非正常的混沌扩散。
