Wang Qian, Robnik Marko
CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI-2000 Maribor, Slovenia.
Department of Physics, Zhejiang Normal University, Jinhua 321004, China.
Entropy (Basel). 2021 Oct 15;23(10):1347. doi: 10.3390/e23101347.
We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate the Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase-space-averaged multifractal dimensions, which are well described by random matrix theory in a strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos.
我们通过在弗洛凯算子本征态的基上展开，给出了受踢陀螺模型中相干态的多重分形分析。我们展示了相干态多重分形性质中相空间结构的表现。在经典极限下，可以构建经典动力学映射，这使我们能够探索相应的相空间图并计算李雅普诺夫指数。通过调节踢动强度，系统经历从规则到混沌的转变。我们表明，相干态的多重分形维数随踢动强度的变化能够捕捉相空间的结构变化。相空间平均多重分形维数清楚地识别出混沌的开始，在强混沌区域，随机矩阵理论能很好地描述这些维数。我们进一步研究展开系数的概率分布，并表明数值结果与随机矩阵理论预测之间的偏差可作为量子混沌的可靠探测器。
