极限循环、固定点与临界减缓的量子起源

在经典耗散动力学中，持久的极限循环振荡以及在此类振荡发生时临界减缓处的纯代数时间 Relaxation 是最著名的特征。另一方面，受一般马尔可夫耗散作用的量子系统会以指数时间退相干，趋于唯一稳定态。 Here we show how coherent limit-cycle oscillations and algebraic decay can emerge in a quantum system governed by a Markovian master equation as one approaches the classical limit, illustrating general mechanisms using a single-spin model and a two-site lossy Bose-Hubbard model. In particular, we demonstrate that the fingerprint of a limit cycle is a slow-decaying branch with vanishing decoherence rates in the Liouville spectrum, while a power-law decay is realized by a spectral collapse at the bifurcation point. 我们也表明这些与经典固定点的区别在于，量子谱是脱节的,并且可以从线性化的经典动力学生成。