标题： 混合系统中的普遍波函数结构 显示英文标题

标题： Universal wave functions structure in mixed systems

摘要： 当一个规则的经典系统受到扰动时，根据KAM定理和Poincaré-Birkhoff定理，会出现非线性共振。 本文研究了这一经典现象在量子波函数形态上的表现。 我们揭示了在具有混合经典动力学的系统中，局域化波函数的普遍结构的系统形成。 未受扰动的状态如果围绕不变环面存在，并且在避免交叉处发生碰撞时，如果它们的量子数在一个经典共振阶数的倍数上不同，则这些状态会混合在一起。 在避免交叉点处，本征态局域化在共振对应的岛屿链中，或者在不稳定周期轨道的附近。 量子数的差异决定了局域化态的激发，这可以通过Husimi分布的零点来揭示。 显示英文摘要

摘要： When a regular classical system is perturbed, non-linear resonances appear as prescribed by the KAM and Poincar\`{e}-Birkhoff theorems. Manifestations of this classical phenomena to the morphologies of quantum wave functions are studied in this letter. We reveal a systematic formation of an universal structure of localized wave functions in systems with mixed classical dynamics. Unperturbed states that live around invariant tori are mixed when they collide in an avoided crossing if their quantum numbers differ in a multiple to the order of the classical resonance. At the avoided crossing eigenstates are localized in the island chain or in the vicinity of the unstable periodic orbit corresponding to the resonance. The difference of the quantum numbers determines the excitation of the localized states which is reveled using the zeros of the Husimi distribution.