Superadiabatic transition histories in quantum molecular dynamics

Abstract

We study the dynamics of a molecule's nuclear wave-function near an avoided crossing of two electronic energy levels, for one nuclear degree of freedom. We derive the general form of the Schroedinger equation in the n-th superadiabatic representation for all n, and give some partial results about the asymptotics for large n. Using these results, we obtain closed formulas for the time development of the component of the wave function in an initially unoccupied energy subspace, when a wave packet crosses the transition region. In the optimal superadiabatic representation, which we define, this component builds up monontonically. Finally, we give an explicit formula for the transition wave function away from the crossing, which is in excellent agreement with high precision numerical calculations.

31 pages, 3 figures

References in corpus (5)

• A Time-Dependent Born-Oppenheimer Approximation with Exponentially Small Error Estimates
• Time Development of Exponentially Small Non-Adiabatic Transitions
• Precise coupling terms in adiabatic quantum evolution: The generic case
• Determination of Non-Adiabatic Scattering Wave Functions in a Born-Oppenheimer Model
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Cited by in corpus (9)

• An Egorov Theorem for avoided crossings of eigenvalue surfaces
• Spontaneous decay of resonant energy levels for molecules with moving nuclei
• Wave packet dynamics in the optimal superadiabatic approximation
• Generation results for vector-valued elliptic operators with unbounded coefficients in L^p spaces
• $L^p$-theory for Schrödinger systems
• Non-adiabatic transitions through tilted avoided crossings
• Non-adiabatic transitions in multiple dimensions
• Vector-valued Schrödinger operators on $L^p$-spaces
• Generation of semigroup for symmetric matrix Schrödinger operators in $L^p$-spaces