论文标题
超级延期Pomeau-Manneville地图中的动态过渡和老化
Dynamical transitions and aging in the superdiffusive Pomeau-Manneville map
论文作者
论文摘要
Pomeau-Manneville地图是一个范式的间歇性动力系统，表现出弱混乱和异常动力学。在本文中，我们分析了地图的超截止量的参数依赖性，该参数定期提升到真实线上。从数值模拟中，我们计算该模型的广义扩散系数（GDC）作为地图非线性参数的函数。我们在GDC中确定了两个奇异的动力转换，一个偏移与无穷大，而第二个完全抑制。使用莱维步道的连续时间随机步行理论，我们计算了GDC的分析表达式，并表明它在质上重现了这两个过渡。数量上它系统地偏离了小参数值的确定性动力学，我们通过速度相关性的缓慢衰减来解释。有趣的是，将老化施加到模拟中的动力学上，消除了导致GDC抑制的动力转变，从而导致了超扩散参数依赖性的非平凡变化。这也适用于显示相关过渡的各个间隔模型的间歇性模型。
The Pomeau-Manneville map is a paradigmatic intermittent dynamical system exhibiting weak chaos and anomalous dynamics. In this paper we analyse the parameter dependence of superdiffusion for the map lifted periodically onto the real line. From numerical simulations we compute the generalised diffusion coefficient (GDC) of this model as a function of the map's nonlinearity parameter. We identify two singular dynamical transitions in the GDC, one where it diverges to infinity, and a second one where it is fully suppressed. Using the continuous-time random walk theory of Lévy walks we calculate an analytic expression for the GDC and show that it qualitatively reproduces these two transitions. Quantitatively it systematically deviates from the deterministic dynamics for small parameter values, which we explain by slow decay of velocity correlations. Interestingly, imposing aging onto the dynamics in simulations eliminates the dynamical transition that led to suppression of the GDC, thus yielding a non-trivial change in the parameter dependence of superdiffusion. This also applies to a respective intermittent model of subdiffusive dynamics displaying a related transition.
