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arXiv:math-ph/0104024 · Communications in Mathematical Physics

Adiabatic Decoupling and Time-Dependent Born–Oppenheimer Theory

Herbert Spohn, Stefan Teufel

Published Nov 1, 2001• 51 citations
arXivHTMLPDF
DOI
10.1007/s002200100535

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We reconsider the time-dependent Born-Oppenheimer theory with the goal to carefully separate between the adiabatic decoupling of a given group of energy bands from their orthogonal subspace and the semiclassics within the energy bands. Band crossings are allowed and our results are local in the sense that they hold up to the rst time when a band crossing is encountered. The adiabatic decoupling leads to an eective Schrodinger equation for the nuclei, including contributions from the Berry connection. 1
A systematic perturbation scheme is developed for approximate solutions to the time-dependent Schroedinger equation with a space-adiabatic Hamiltonian. For a particular isolated energy band, the basic approach is to separate kinematics from dynamics. The kinematics is defined through a subspace of the full Hilbert space for which transitions to other band subspaces are suppressed to all orders and the dynamics operates in that subspace in terms of an effective intraband Hamiltonian. As novel applications we discuss the Born-Oppenheimer theory to second order and derive the nonperturbative definition of the g-factor of the electron within nonrelativistic quantum electrodynamics.