Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina and Departamento de Física, FCEyN, Universidad de Buenos Aires, C1428EGA, Argentina.
Departamento de Física, CNEA, CONICET, Libertador 8250, (C1429BNP) Buenos Aires, Argentina.
Phys Rev E. 2017 Dec;96(6-1):062144. doi: 10.1103/PhysRevE.96.062144. Epub 2017 Dec 26.
We study a generic and paradigmatic two-degrees-of-freedom system consisting of two coupled perturbed cat maps with different types of dynamics. The Wigner separability entropy (WSE)-equivalent to the operator space entanglement entropy-and the classical separability entropy (CSE) are used as measures of complexity. For the case where both degrees of freedom are hyperbolic, the maps are classically ergodic and the WSE and the CSE behave similarly, growing to higher values than in the doubly elliptic case. However, when one map is elliptic and the other hyperbolic, the WSE reaches the same asymptotic value than that of the doubly hyperbolic case but at a much slower rate. The CSE only follows the WSE for a few map steps, revealing that classical dynamical features are not enough to explain complexity growth.
我们研究了一个由两个具有不同动力学类型的耦合受扰猫映射组成的通用范例性两自由度系统。Wigner 可分离熵（WSE）——相当于算子空间纠缠熵——和经典可分离熵（CSE）被用作复杂性的度量。对于两个自由度都是双曲的情况，映射是经典遍历的，WSE 和 CSE 的行为相似，增长到比双椭圆情况下更高的值。然而，当一个映射是椭圆的而另一个是双曲的时，WSE 达到与双双曲情况相同的渐近值，但速度要慢得多。CSE 仅在几个映射步骤中遵循 WSE，这表明经典动力学特征不足以解释复杂性的增长。
