Semi-classical approximation for time-dependent systems

Clotilde Fermanian Kammerer (UPEC)

Jun 13. 2023, 15:00 — 15:50

We discuss in this talk the construction of initial value representations of solutions of systems of semi-classical equations given by a time-dependent matrix-valued Hamiltonian. Such systems could arise in mathematical relativity from a linearization process. These initial value representations are inspired by the approach of the theoretical chemists Herman and Kluk who propagated continuous superpositions of Gaussian wave-packets for scalar equations. We explain how to generalize their construction to systems, including those presenting (smooth) eigenvalue crossings by incorporating to classical transport a branching process along a hopping hypersurface.  We also explain how these propagators give an algorithmic approximated description of the propagator. 


Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Spectral Theory and Mathematical Relativity (Thematic Programme)
Piotr T. Chruściel (U of Vienna)
Peter Hintz (ETH Zurich)
Alexander Strohmaier (U Leeds)
Steven Morris Zelditch † (Northwestern U Evanston)