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Explore the quantum mechanics of two-component systems through this 56-minute lecture that presents a unified approach to non-adiabatic phenomena using exact factorization methods. Learn how quantum systems with particles of vastly different masses, such as electrons and nuclei, can be treated beyond the traditional Born-Oppenheimer approximation to understand fascinating phenomena like the microscopic processes in vision and electronic decoherence that prevents scalable quantum computing. Discover the exact factorization approach that represents the full electron-nuclear wave function as a product of a nuclear component and a parametrically dependent many-electron wave function, providing an ideal foundation for developing efficient algorithms to study non-adiabatic phenomena. Examine the development of time-dependent density functional theory for complete electron-nuclear systems, including the resulting time-dependent Kohn-Sham equations with their unique non-unitary time evolution essential for describing decoherence and their ability to create electron correlations through non-adiabatic nuclear interactions. See practical applications demonstrated through vibrational circular dichroism descriptions, ab-initio decoherence evaluations, and beyond-Born-Oppenheimer molecular Berry phase calculations that showcase this method's power for arbitrary two-component systems.
