Space-adiabatic Decoupling to All Orders

TL;DR

This paper develops a systematic perturbation method for solving the time-dependent Schrödinger equation with space-adiabatic Hamiltonians, enabling precise band separation and effective intraband dynamics analysis.

Contribution

It introduces a comprehensive perturbation scheme for space-adiabatic systems, including applications to Born-Oppenheimer theory and electron g-factor calculation in QED.

Findings

Transitions between energy bands are suppressed to all orders.

The method provides a nonperturbative definition of the electron g-factor.

Application to second-order Born-Oppenheimer theory.

Abstract

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.