Plenary talk of Christian Lubich (Universität Tübingen)

Variational approximations in quantum dynamics and the MCTDH method
The talk describes model reduction in the multi-particle time-dependent Schrödinger equation via the Dirac-Frenkel variational approximation principle and then turns to the multi-configuration time-dependent Hartree method (MCTDH) as an important, practically very successful example. This approach can be viewed as a dynamical low-rank approximation to the high-dimensional wave function. The nonlinear, but low-dimensional MCTDH equations of motion and their numerical integration are discussed. The talk closes with an analysis of the modelling error in the MCTDH method, showing the mechanisms that may lead to convergence or failure.


Lars Grasedyck (MPI Leipzig, Germany)
Wolfgang Hackbusch (MPI Leipzig, Germany)
Boris Khoromskij (MPI Leipzig, Germany)