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

Journal Article · Mon Feb 15 00:00:00 EST 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.022510· OSTI ID:21408226

Balzer, K; Bauch, S; Bonitz, M ^[1]

---

1. Institut fuer Theoretische Physik und Astrophysik, Christian-Albrechts-Universitaet Kiel, Leibnizstrasse 15, 24098 Kiel (Germany)

The finite-element discrete variable representation is proposed 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 toward a direct solution of the two-time Schwinger-Keldysh-Kadanoff-Baym equations on spatial grids, including, for example, the description of highly excited states in atoms. As benchmarks, we compute and characterize, in Hartree-Fock and second Born approximations, the ground states of the He atom, the H{sub 2} molecule, and the LiH molecule in one spatial dimension. Thereby, the ground-state and binding energies, densities, and bond lengths are compared with the direct solution of the time-dependent Schroedinger equation.

• OSTI ID: 21408226
• Journal Information: Physical Review. A, Vol. 81, Issue 2; Other Information: DOI: 10.1103/PhysRevA.81.022510; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ATOMS
BINDING ENERGY
BOND LENGTHS
BORN APPROXIMATION
EXCITED STATES
FINITE ELEMENT METHOD
GREEN FUNCTION
GROUND STATES
HARTREE-FOCK METHOD
HELIUM
LITHIUM HYDRIDES
MOLECULES
SCHROEDINGER EQUATION
ALKALI METAL COMPOUNDS
APPROXIMATIONS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
DIMENSIONS
ELEMENTS
ENERGY
ENERGY LEVELS
EQUATIONS
FLUIDS
FUNCTIONS
GASES
HYDRIDES
HYDROGEN COMPOUNDS
LENGTH
LITHIUM COMPOUNDS
MATHEMATICAL SOLUTIONS
NONMETALS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
RARE GASES
WAVE EQUATIONS