论文标题
在踢哈珀模型中的扩散开始
On the onset of diffusion in the kicked Harper model
论文作者
论文摘要
我们通过拓扑论证和kaM理论的结合研究了一个标准的两参数家族，在理论物理学中被称为踢哈珀模型。我们集中于旋转集分别具有空内部和非空内部的参数集的结构，并描述了其定性属性和针对小参数的定性属性和缩放行为。这证实了关于物理文献中扩散发作的数值观察。作为副产品，我们获得了在哈密顿圆环同构中的旋转集的连续性。
We study a standard two-parameter family of area-preserving torus diffeomorphisms, known in theoretical physics as the kicked Harper model, by a combination of topological arguments and KAM-theory. We concentrate on the structure of the parameter sets where the rotation set has empty and non-empty interior, respectively, and describe their qualitative properties and scaling behaviour both for small and large parameters. This confirms numerical observations about the onset of diffusion in the physics literature. As a byproduct, we obtain the continuity of the rotation set within the class of Hamiltonian torus homeomorphisms.
