Kłobus Waldemar, Kurzyński Paweł, Kuś Marek, Laskowski Wiesław, Przybycień Robert, Życzkowski Karol
Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308 Gdańsk, Poland.
Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland.
Phys Rev E. 2022 Mar;105(3-1):034201. doi: 10.1103/PhysRevE.105.034201.
We study a damped kicked top dynamics of a large number of qubits (N→∞) and focus on an evolution of a reduced single-qubit subsystem. Each subsystem is subjected to the amplitude damping channel controlled by the damping constant r∈[0,1], which plays the role of the single control parameter. In the parameter range for which the classical dynamics is chaotic, while varying r we find the universal period-doubling behavior characteristic to one-dimensional maps: period-2 dynamics starts at r_{1}≈0.3181, while the next bifurcation occurs at r_{2}≈0.5387. In parallel with period-4 oscillations observed for r≤r_{3}≈0.5672, we identify a secondary bifurcation diagram around r≈0.544, responsible for a small-scale chaotic dynamics inside the attractor. The doubling of the principal bifurcation tree continues until r≤r_{∞}∼0.578, which marks the onset of the full scale chaos interrupted by the windows of the oscillatory dynamics corresponding to the Sharkovsky order. Finally, for r=1 the model reduces to the standard undamped chaotic kicked top.
我们研究了大量量子比特（(N\to\infty)）的阻尼踢顶动力学，并关注一个约化的单量子比特子系统的演化。每个子系统都受到由阻尼常数(r\in[0,1])控制的振幅阻尼通道的影响，该阻尼常数充当单一控制参数的角色。在经典动力学为混沌的参数范围内，当改变(r)时，我们发现了一维映射特有的通用倍周期行为：2周期动力学始于(r_1\approx0.3181)，而下一个分岔发生在(r_2\approx0.5387)。与(r\leq r_3\approx0.5672)时观察到的4周期振荡并行，我们在(r\approx0.544)附近识别出一个二级分岔图，它导致吸引子内部出现小尺度混沌动力学。主分岔树的倍化持续到(r\leq r_{\infty}\sim0.578)，这标志着全尺度混沌的开始，该混沌被对应于沙可夫斯基序的振荡动力学窗口打断。最后，对于(r = 1)，该模型简化为标准的无阻尼混沌踢顶。
