We study the fluctuation-activated transition process in a system of two coupled bistable oscillators, in which each oscillator is driven by one constant force and an independent Gaussian white noise. The transition pathway has been identified and the transition rate has been computed as the coupling strength $μ$ and the mismatch $σ$ in the force constants are varied. For identical oscillators ($σ=0$), the transition undergoes a change from a two-step process with two candidate pathways to a one-step process with also two candidate pathways to a one-step process with a single pathway as $μ$ is increased. For nonidentical oscillators ($σ\neq0$), a novel transition emerges that is a mixture of a two-step pathway and a one-step pathway. Interestingly, we find that the total transition rate depends nonmonotonically on $μ$: a maximal rate appears in an intermediate magnitude of $μ$. Moreover, in the presence of weak coupling the rate also exhibits an unexpected maximum as a function of $σ$. The results are in an excellent agreement with our numerical simulations by forward flux sampling.
Quantum approach to the thermalization of the toppling pencil interacting with a finite bath
我们研究了长期存在的问题，热化的量子系统耦合到一个环境，通过专注于一个四次振子与有限数量的谐振子相互作用。为了克服指数墙，人们通常遇到的网格为基础的方法来解决扩展系统的时间相关的薛定谔方程，方法的时间相关的变分原理是最适合的。这里我们将应用耦合相干态的方法[D. V. Shalashilin和M. S. Child，J. Chem. Phys. { \bf 113}，10028（2000）]。通过研究双势阱势垒顶部的初始波函数的动力学，将表明，只有少数具有适当选择的频率的振荡器，从它们的基态开始，就足以驱动双势阱系统接近其非耦合的基态。双阱能量的长时间平均值被发现是一个单调衰减的函数的参数范围内的环境振荡器的数量是数字访问。
Spontaneous synchronization of coupled oscillator systems with frequency adaptation
我们研究了仓本振子的同步与所有的所有耦合在存在缓慢的，嘈杂的频率适应。在本文中，我们开发了一个新的模型，适应他们的相位和频率的振荡器。结果发现，该模型自然地再现了一些观察到的现象，而不是定性产生的标准仓本模型，如长时间的等待时间之前，鼓掌观众的同步。通过自洽定态解的假设，我们发现了耦合常数k的三个稳定区域，它们由临界点k1和k2分开：（i）当k<k1时，只存在稳定的非相干态;（ii）当k>k2时，非相干态变得不稳定，只存在同步态;（iii）当k1<k<k2时，非相干态和同步态都是稳定的。在非相干态和同步态之间的自发跃迁观察到有限的合奏。这些跃迁被描述为一个关于序参量r的随机过程，由于系统的有限尺寸，这些随机过程经历了涨落，从而得到以下结论：（a）在非相干区，非相干到相干跃迁的平均等待时间可以用Kramer的逃逸时间公式来预测，并且随着振子的数目呈指数增长;（b）当非相干态不稳定时（k> k ~ 2），平均等待时间随振子个数的增加而呈指数增长。
