Finite elements and the discrete variable representation in nonequilibrium Green's function calculations. Atomic and molecular models

TL;DR

This paper introduces an efficient finite-element discrete variable representation for nonequilibrium Green's function calculations, significantly speeding up the computation of self-energies in atomic and molecular models.

Contribution

It presents a novel FE-DVR approach that enhances the efficiency of solving two-time quantum Green's function equations for inhomogeneous systems.

Findings

FE-DVR leads to substantial speedup in self-energy calculations.

Accurate ground-state properties for He atom and H3+ in 1D are obtained.

Results agree well with exact solutions from the time-dependent Schrödinger equation.

Abstract

In this contribution, we discuss the finite-element discrete variable representation (FE-DVR) of the nonequilibrium Green's function and its implications on the description of strongly inhomogeneous quantum systems. In detail, we show that the complementary features of FEs and the DVR allows for a notably more efficient solution of the two-time Schwinger/Keldysh/Kadanoff-Baym equations compared to a general basis approach. Particularly, the use of the FE-DVR leads to an essential speedup in computing the self-energies. As atomic and molecular examples we consider the He atom and the linear version of H$_3^+$ in one spatial dimension. For these closed-shell models we, in Hartree-Fock and second Born approximation, compute the ground-state properties and compare with the exact findings obtained from the solution of the few-particle time-dependent Schr\"odinger equation.