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Explore a comprehensive lecture on semi-classical approximation for time-dependent systems presented by Clotilde Fermanian Kammerer at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the construction of initial value representations for solutions of semi-classical equations with time-dependent matrix-valued Hamiltonians, which have potential applications in mathematical relativity. Examine the generalization of Herman and Kluk's approach, originally developed for scalar equations, to systems with smooth eigenvalue crossings. Discover how classical transport is combined with a branching process along a hopping hypersurface to handle these complex systems. Gain insights into the algorithmic approximated description of the propagator derived from these methods. This one-hour talk, part of the Thematic Programme on "Spectral Theory and Mathematical Relativity," offers a deep dive into advanced mathematical techniques at the intersection of quantum mechanics and relativity.
