量子 Stuart-Landau 振荡器的瞬态动力学
Transient dynamics of the quantum Stuart-Landau oscillator
AI总结：
本文研究了量子 Stuart-Landau 振荡器的瞬态动力学，通过推导 Wigner 函数运动方程、分析非经典性指标及 Liouvillian 谱，揭示了不同初始态达到稳态的时间差异，为自持量子系统瞬态行为提供了深刻见解。
摘要：
我们研究了量子 Stuart-Landau 振荡器的瞬态动力学，这是一个展示量子极限环和同步现象的典型量子系统。从能量动力学出发，我们确定了瞬态动力学和极限环的经典区域条件。此外，我们构建了一个拟合经典区域稳态 Wigner 函数的猜测函数。我们推导了 Wigner 函数的运动方程，并将其与随机过程的 Kramers-Moyal 方程进行了比较。随后，我们表征了系统从相干态演化时的类经典行为，并注意到相邻能级相干性的缓慢衰减。我们还研究了 Wigner 负性作为非经典性指标的演化，表明在某些特定情况下它会暂时增加。为了量化演化速度，我们考察了系统的 Lindbladian 谱，特别是 Liouvillian 间隙。最后，我们记录了某些 Fock 态、热态和相干态达到稳态所需的时间。稳态时间的参数依赖性可能与 Liouvillian 间隙不同，并且与 Fock 态或热态相比，相干态的极限环吸引显著更慢。对于对角态，存在快速收敛区域，使得稳态时间在局部达到最小值。本研究为自持量子系统的瞬态行为提供了更深刻的见解。
英文摘要：
We investigate the transient dynamics of the quantum Stuart-Landau oscillator, a paradigmatic quantum system exhibiting a quantum limit cycle and synchronization. From the energy dynamics, we determine a condition for the classical regime of transient dynamics and the limit cycle. Additionally, we formulate a guess function that fits the classical-regime steady-state Wigner function. The equation of motion for the Wigner function is derived and compared to the Kramers-Moyal equation for stochastic processes. We then characterize the classical-like behavior as the system evolves from a coherent state, noting the slow decay of neighboring-level coherence. We also study the evolution of the Wigner negativity as an indicator of nonclassicality, showing its temporary increase for some specific cases. To quantify the evolution speed, we examined the system's Lindbladian spectra, particularly the Liouvillian gap. Finally, we record the time it takes to reach the steady state for some Fock, thermal, and coherent states. The parameter dependence of the steady-state time may differ from the Liouvillian gap, and the limit-cycle attraction is significantly slower for coherent states compared to Fock or thermal states. For the diagonal states, there are \revision{fast convergence regimes} for which the steady-state time is locally minimized. This study provides a deeper insight into the transient behavior of self-sustained quantum systems.
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