Efficient grid-based method in nonequilibrium Green's function calculations. Application to model atoms and molecules

Abstract

We propose and apply the finite-element discrete variable representation to express the nonequilibrium Green's function for strongly inhomogeneous quantum systems. This method is highly favorable against a general basis approach with regard to numerical complexity, memory resources, and computation time. Its flexibility also allows for an accurate representation of spatially extended hamiltonians, and thus opens the way towards a direct solution of the two-time Schwinger/Keldysh/Kadanoff-Baym equations on spatial grids, including e.g. the description of highly excited states in atoms. As first benchmarks, we compute and characterize, in Hartree-Fock and second Born approximation, the ground states of the He atom, the H${}_2$ molecule and the LiH molecule in one spatial dimension. Thereby, the ground-state/binding energies, densities and bond-lengths are compared with the direct solution of the time-dependent Schrödinger equation.

11 pages, 5 figures, submitted to Physical Review A

References in corpus (5)

• Kadanoff-Baym approach to quantum transport through interacting nanoscale systems: From the transient to the steady-state regime
• Time-propagation of the Kadanoff-Baym equations for inhomogeneous systems
• Impact of Exchange-Correlation Effects on the IV Characteristics of a Molecular Junction
• Rabi Oscillations and Few-Level Approximations in Time-Dependent Density Functional Theory
• Quantum kinetic approach to time-resolved photoionization of atoms

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