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

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 Schrödinger equation.

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

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Cited by in corpus (4)

• Time-dependent generalized-active-space configuration-interaction approach to photoionization dynamics of atoms and molecules
• Time-dependent second Born calculations for model atoms and molecules in strong laser fields
• Ultrafast Dynamics of Strongly Correlated Fermions -- Nonequilibrium Green Functions and Selfenergy Approximations
• Efficient computation of the second-Born self-energy using tensor-contraction operations