Construction of Solution Landscape for Complex Systems

Explore the innovative concept of "Solution Landscape" in this conference talk by Lei Zhang at #ICBS2024. Delve into a novel approach to searching for stationary states on energy landscapes without relying on random guesses. Learn about the saddle dynamics method for constructing solution landscapes, which provides a comprehensive pathway map of all stationary points and their connections. Discover how this approach not only identifies all possible minima but also enhances our understanding of complex system movements on energy landscapes. Examine practical applications of the solution landscape approach, including investigations into defect landscapes of nematic liquid crystals, transition pathways between crystalline and quasicrystalline phases, and excited states of rotational Bose–Einstein condensates. Gain insights into this groundbreaking technique that addresses a long-standing problem in computational mathematics and physics.