Time-dependent natural orbitals and occupation numbers

TL;DR

This paper derives equations for the time evolution of natural orbitals and occupation numbers, highlighting limitations of existing functionals and demonstrating their dynamic behavior in electron-ion scattering and laser-atom interactions.

Contribution

It introduces equations of motion for occupation numbers and shows that common adiabatic functionals fail to capture their time dependence.

Findings

Occupation numbers vary significantly over time in laser fields.

Adiabatic functionals lead to time-independent occupation numbers.

Exact solutions show dynamic behavior of natural orbitals and occupation numbers.

Abstract

We report equations of motion for the occupation numbers of natural spin orbitals and show that adiabatic extensions of common functionals employed in ground-state reduced-density-matrix-functional theory have the shortcoming of leading always to occupation numbers which are independent of time. We illustrate the exact time-dependence of the natural spin orbitals and occupation numbers for the case of electron-ion scattering and for atoms in strong laser fields. In the latter case, we observe strong variations of the occupation numbers in time.