AI 中文总结
该研究从理论上探究了与正常金属柱耦合的可移动库珀对盒的动力学，通过分析非线性纳米机电耦合诱导的稳定性，揭示了其在不同η下的霍普夫分岔特性，扩展了自振动研究的适用区域并得到了丰富的动力学相图。
AI 中文摘要
我们采用半经典方法从理论上研究了与正常金属柱耦合的可移动库珀对盒的动力学。通过线性稳定性和分岔分析，我们分析了由机械运动与非弹性安德烈夫隧穿之间的非线性纳米机电耦合诱导的动力学稳定性。作为η（定义为静电能与约瑟夫森耦合能的比值）的函数，系统表现出重入稳定性。在小η时，不动点通过超临界霍普夫分岔失去稳定性，从而产生自持振动。随着η的进一步增加，会出现第二个临界点，此时不动点恢复稳定性。我们表明，在绝热区域中，第二次转变对应于逆亚临界霍普夫分岔，而在非绝热区域中对应于逆超临界霍普夫分岔。这些结果将先前对绝热自振动的研究扩展到了非绝热区域，并揭示了超导器件中电子自由度与机械自由度相互作用产生的丰富非线性动力学相图。
英文摘要
We theoretically study the dynamics of a movable Cooper-pair box coupled to a normal-metal pillar using a semiclassical approach. We analyze the dynamical stability induced by the nonlinear nanoelectromechanical coupling between the mechanical motion and an inelastic Andreev tunneling through linear stability and bifurcation analyses. As a function of $η$, defined as the ratio of electrostatic energy to Josephson coupling energy, the system exhibits reentrant stability. At small $η$, the fixed point loses stability through a supercritical Hopf bifurcation, giving rise to self-sustained vibrations. With a further increase of $η$, a second critical point appears, at which the fixed point regains stability. We show that this second transition corresponds to an inverse subcritical Hopf bifurcation in the adiabatic regime and to an inverse supercritical Hopf bifurcation in the nonadiabatic regime. These results extend previous studies of adiabatic self-vibrations to the nonadiabatic regime and reveal a rich nonlinear dynamical phase diagram arising from the interplay between electronic and mechanical degrees of freedom in superconducting devices.
Comments8 pages, 1 figure
