弱噪声极限下振荡的相干性
Coherence of oscillations in the weak-noise limit
AI总结：
该研究在弱噪声极限下解析推导了一维周期势受驱福克-普朗克振荡的品质因子，证明了连续模型的相干性上界，方法可拓展至二维极限环系统，补充了哈密顿-雅可比理论框架。
摘要：
在噪声环境中，振荡会失去相干性，这一特性可用品质因子来表征。我们针对受驱Fokker-Planck（福克-普朗克）动力学沿一维周期势产生的振荡，在弱噪声极限下解析推导了该品质因子。借助这一表达式，我们证明了该连续模型中存在一个上界的类似结论，该上界是此前针对离散Markov（马尔可夫）网络模型中振荡相干性提出的猜想。我们的方法也可适配于噪声作用下二维极限环的运动。具体而言，我们将该方案应用于含噪声的Stuart-Landau（斯图尔特-朗道）振子，以及作为化学时钟简单模型的热力学自洽Brusselator（布鲁塞尔振子）。因此，我们的方法补充了现有基于Hamilton-Jacobi（哈密顿-雅可比）理论技术的相当成熟的通用框架，我们还通过数值计算将结果与该框架进行了对比。
英文摘要：
In a noisy environment, oscillations loose their coherence which can be characterized by a quality factor. We determine this quality factor for oscillations arising from a driven Fokker-Planck dynamics along a periodic one-dimensional potential analytically in the weak noise limit. With this expression, we can prove for this continuum model the analog of an upper bound that has been conjectured for the coherence of oscillations in discrete Markov network models. We show that our approach can also be adapted to motion along a noisy two-dimensional limit cycle. Specifically, we apply our scheme to the noisy Stuart-Landau oscillator and the thermodynamically consistent Brusselator as a simple model for a chemical clock. Our approach thus complements the fairly sophisticated extant general framework based on techniques from Hamilton-Jacobi theory with which we compare our results numerically.
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