论文标题
扩散方程的应用以证明从限制到无限扩散的过渡上的扩展不变性
Application of the diffusion equation to prove scaling invariance on the transition from limited to unlimited diffusion
论文作者
论文摘要
通过扩散方程的分析解决方案来解释从无限到有限扩散的过渡到有限扩散的过渡附近的混乱轨道的缩放不变性。它给出了在给定时间观察具有特定动作的粒子的概率。我们显示的扩散系数随时间而变化缓慢，并负责抑制无限的扩散。确定概率的矩，并获得平均平方作用的行为。小时和大的限制从现象学方法中恢复了文献中已知的结果，并且作为奖励，中间时间的缩放是取决于初始作用的。提出的形式主义足够强大，可以应用于其他各种系统中，包括从有限的台球到从有限的台球到无限的费米加速度的过渡，正如我们在字母结束时和许多其他系统在耗散存在以及从集成性到不集成性的过渡相近的其他系统中所示。
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a particle with a specific action at a given time. We show the diffusion coefficient varies slowly with the time and is responsible to suppress the unlimited diffusion. The momenta of the probability are determined and the behavior of the average squared action is obtained. The limits of small and large time recover the results known in the literature from the phenomenological approach and, as a bonus, a scaling for intermediate time is obtained as dependent on the initial action. The formalism presented is robust enough and can be applied in a variety of other systems including time dependent billiards near a transition from limited to unlimited Fermi acceleration as we show at the end of the letter and in many other systems under the presence of dissipation as well as near a transition from integrability to non integrability.
