🤖 AI Summary
This study addresses the inverse problem of inferring the statistical properties of an unknown, complex energy landscape from the dynamical response of a system traversing it, with particular emphasis on the stability of metastable states against thermal activation and quantum tunneling. By modeling the potential energy surface as a Gaussian random field and integrating path integral formalism with statistical mechanics, the work establishes—for the first time—a quantitative relationship between transition rates and the Green’s function of the underlying potential. Building on this framework, the authors derive the joint probability distribution of local potential characteristics—such as value, gradient, and curvature—and propose a novel paradigm for reconstructing the statistical structure of the energy landscape directly from observed activation dynamics. This approach provides a rigorous theoretical foundation for spectral modeling of complex energy landscapes in disordered and glassy systems.
📝 Abstract
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.