Abstract

Transition state theory (TST) is a powerful framework to describe reactions which are mediated by a transition state between reactants and products. Due to its formulation in phase space and its general assumptions, it has numerous applications in chemistry and physics. However, because there exists no such phase space in the Schrödinger theory, TST cannot be applied directly to spatially extended wave packets as they appear in several quantum mechanical systems.

In this talk, I will present a general method which allows for the application of TST to the dynamics of quantum wave packets in a variational framework. Within the latter, the original wave function is replaced by an appropriate trial wave function depending on a set of variational parameters, and the Schrödinger equation is approximately solved by applying a time-dependent variational principle. The latter defines a noncanonical Hamiltonian system for the variational parameters, in which common structures such as ground or transition states, dividing surfaces, reactants and products can be identified.

In order to construct a dividing surface which is free of local recrossings, a normal form expansion in variational space is performed. The latter’s generating function can be chosen in such a way that it extracts the normal form of the dynamical equations as well as canonical coordinates in a natural way. The resulting classical Hamiltonian then directly allows to apply TST to the quantum system. Applications of the method will be demonstrated for a model potential within the linear Schrödinger theory and for Bose-Einstein condensates as nonlinear Schrödinger systems.