Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules

We construct an abstract pseudodifferential calculus with operator-valued symbol, adapted to the treatment of Coulomb-type interactions, and we apply it to study the quantum evolution of molecules in the Born-Oppenheimer approximation, in the case where the electronic Hamiltonian admits a local gap in its spectrum. In particular, we show that the molecular evolution can be reduced to the one of a system of smooth semiclassical operators, the symbol of which can be computed explicitely. In addition, we study the propagation of certain wave packets up to long time values of Ehrenfest order. (This work has been accepted for publication as part of the Memoirs of the American Mathematical Society and will be published in a future volume.)Comment: 73 page

On the Born-Oppenheimer approximation of diatomic molecular resonances

We give a new reduction of a general diatomic molecular Hamiltonian, without modifying it near the collision set of nuclei. The resulting effective Hamiltonian is the sum of a smooth semiclassical pseudodifferential operator (the semiclassical parameter being the inverse of the square-root of the nuclear mass), and a semibounded operator localised in the elliptic region corresponding to the nuclear collision set. We also study its behaviour on exponential weights, and give several applications where molecular resonances appear and can be well located.Comment: 22 page

Molecular Scattering and Born-Oppenheimer Approximation

In this paper, we study the scattering wave operators for a diatomic molecules by using the Born-Oppenheimer approximation. Assuming that the ratio h^2 between the electronic and nuclear masses is small, we construct adiabatic wave operators that, under some non trapping conditions, approximate the two-cluster wave operators up to any powers of the parameter