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

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

2009-11-23

arxiv.org/abs/0911.4348v1

Physics

Condensed Matter

Strongly Correlated Electrons

12 pages, 3 figures, submitted as proceedings of conference "PNGF IV"

Scientific paper

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.

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