| Abstract: |
| Energy landscape has been widely applied to many physical and biological systems. A long standing problem in computational mathematics and physics is how to search for the entire family tree of possible stationary states on the energy landscape without unwanted random guesses? Here we introduce a novel concept Solution Landscape, which is a pathway map consisting of all stationary points and their connections. We develop a generic and efficient saddle dynamics method to construct the solution landscape, which not only identifies all possible minima, but also advances our understanding of how a complex system moves on the energy landscape. We then apply the solution landscape approach to target several problems, including the defect landscapes of nematic liquid crystals, the transition pathways connecting crystalline and quasicrystalline phases, and the excited states of rotational Bose-Einstein condensates. |
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