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arXiv · 0911.4348

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

Karsten Balzer·Sebastian Bauch·Michael Bonitz
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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.

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Karsten Balzer, Sebastian Bauch, Michael Bonitz. 2009-11-23. Finite elements and the discrete variable representation in nonequilibrium Green's function calculations. Atomic and molecular models. https://doi.org/10.1088/1742-6596/220/1/012020

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