随机势对热激活和量子激活的统计稳定性
Statistical stability of random potentials to thermal and quantum activation
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中文总结 AI 辅助
本文研究随机势对热与量子激活的统计稳定性，针对高斯随机流形推导势特征统计概率的代数表达式，关联激活速率与势的格林函数，可通过激活行为获取格林函数信息。
中文摘要 AI 辅助
在众多物理、化学和生物系统中，动力学可简化为状态变量在复杂势场中的运动。若该流形已知，嵌入物体的运动和响应可确定性描述，仅受与噪声相关的随机效应影响；反之，若流形未知，状态变量的静态与动态响应可作为光谱工具表征势场。受L. Embon及其合作者的开创性工作[Sci. Rep. 5, 7598 (2015)]启发，我们研究势极小值的统计性质，特别是其对热激活和量子激活的稳定性。针对高斯随机流形，我们推导了代数表达式以评估势特征（值、斜率、曲率等）的统计概率；利用该工具，我们计算了热激活和量子激活速率的期望值，并将这些结果与高斯势的主要特征（即其格林函数）关联起来。这种关联提供了一种途径，可通过研究物体在该流形中的激活行为来获取势的格林函数信息。
英文摘要
In numerous physical, chemical, and biological systems the dynamics can be reduced to the motion of state variables in a complex potential landscape. In case the manifold is known, the motion and response of the embedded object can be described deterministically up to stochastic effects usually associated with a noise. In contrast, if the manifold is unknown, the static and dynamic response of the state variable may be used as a spectroscopic tool to characterize the potential landscape. Inspired by a seminal work of L.\ Embon and co-workers, [Sci.\ Rep.\ \textbf{5}, 7598 (2015)] we investigate the statistical properties of potential minima, in particular, their stability to thermal and quantum activation. For Gaussian random manifolds, we derive an algebraic expression to evaluate the statistical probability of the potential character (value, slope, curvature, ...). With this tool, we compute the expectation value for the rate of thermal and quantum activation and link these findings to the principal characteristics of the Gaussian potential, i.e., its Green's function. This link provides the opportunity to access information on the potential's Green's function by studying the activation behavior of an object in this manifold.
