Adiabatic perturbation theory for two-component systems with one heavy component

TL;DR

This paper develops an adiabatic perturbation theory for two-component quantum systems with a heavy component, deriving an effective Hamiltonian accurate to second order, with applications to electron-nuclei systems.

Contribution

It introduces a new perturbation approach and an effective Hamiltonian with a Hermitian mass tensor and complex vector potential for two-component systems.

Findings

Effective Hamiltonian accurate to second order in inverse heavy mass.

Numerical verification in a diatomic molecule model.

Analytical validation in a vibronic coupling model.

Abstract

Perturbation theory with respect to the kinetic energy of the heavy component of a two-component quantum system is introduced. An effective Hamiltonian that is accurate to second order in the inverse heavy mass is derived. It contains a new form of kinetic energy operator with a Hermitian mass tensor and a complex-valued vector potential. All of the potentials in the effective Hamiltonian can be expressed in terms of covariant derivatives and a resolvent operator. The most salient application of the theory is to systems of electrons and nuclei. The accuracy of the theory is verified numerically in a model diatomic molecule and analytically in a vibronic coupling model.