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arXiv · 1909.13182

Construction of a pathway map on a complicated energy landscape

Jianyuan Yin·Yiwei Wang·Jeff Z. Y. Chen·Pingwen Zhang·Lei Zhang
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Abstract

How do we search for the entire family tree without unwanted random guesses, starting from a high-index and high-energy stationary state on the energy landscape? Here we introduce a general numerical method that constructs the pathway map clearly connecting all stationary points branched from a single parent state. The map guides our understanding of how a physical system moves on the energy landscape. In particular, the method allows us to identify the transition state between energy minima and the energy barrier associated with such a state. As an example, we solve the Landau-de Gennes energy incorporating the Dirichlet boundary conditions to model a liquid crystal confined in square box; we illustrate the basic concepts by examining the multiple stationary solutions and the connected pathway maps of the model.

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Jianyuan Yin, Yiwei Wang, Jeff Z. Y. Chen, Pingwen Zhang, Lei Zhang. 2021-04-20. Construction of a pathway map on a complicated energy landscape. https://doi.org/10.1103/physrevlett.124.090601

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