相对路径概率和随机行为的实验测量
Experimental measurement of relative path probabilities and stochastic actions
摘要：
对于扩散随机动力学，观察到任何单个轨迹的概率都非常小，因此不清楚如何通过实验验证路径概率比的理论结果。我们提供了理论和实验之间的缺失环节，通过建立一个协议，从测量的时间序列中提取路径概率的比率。对于一个单一的胶体颗粒在微通道中的实验，我们提取两个比率的路径概率，和最可能的路径的障碍交叉，并找到良好的协议与独立计算的预测的基础上Onsager-Machlup随机行动。我们在室温下的实验结果与低噪声Freidlin-Wentzell随机作用量不一致，并讨论了在何种情况下后者才能描述最可能的路径.此外，虽然实验可达的路径概率比是唯一确定的，但已知形式路径积分作用量依赖于用于推导它的时间离散方案;通过仔细分析路径积分的时间分片推导，我们调和了这两个看似矛盾的事实。我们的实验协议使我们能够探测路径空间上的概率分布，并使我们能够将理论上的单轨迹结果与测量结果联系起来。
英文摘要：
For diffusive stochastic dynamics, the probability to observe any individual trajectory is vanishingly small, making it unclear how to experimentally validate theoretical results for ratios of path probabilities. We provide the missing link between theory and experiment, by establishing a protocol to extract ratios of path probabilities from measured time series. For experiments on a single colloidal particle in a microchannel, we extract both ratios of path probabilities, and the most probable path for a barrier crossing, and find excellent agreement with independently calculated predictions based on the Onsager-Machlup stochastic action. Our experimental results at room temperature are found to be inconsistent with the low-noise Freidlin-Wentzell stochastic action, and we discuss under which circumstances the latter is expected to describe the most probable path. Furthermore, while the experimentally accessible ratio of path probabilities is uniquely determined, the formal path-integral action is known to depend on the time-discretization scheme used for deriving it; we reconcile these two seemingly contradictory facts by careful analysis of the time-slicing derivation of the path integral. Our experimental protocol enables us to probe probability distributions on path space, and allows us to relate theoretical single-trajectory results to measurement.
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