Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules

Details Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules

2008-09-22

arxiv.org/abs/0809.3663v1

Mathematics

Analysis of PDEs

73 pages

Scientific paper

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.)

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