Stuttgart 2012 – wissenschaftliches Programm

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A: Fachverband Atomphysik

A 26: Poster: Atomic systems in external fields

A 26.5: Poster

Mittwoch, 14. März 2012, 16:30–19:00, Poster.V

Treatment of spatially inhomogeneous, finite systems with the Generalized Kadanoff–Baym Ansatz — •Sebastian Hermanns, Karsten Balzer, and Michael Bonitz — Institut für Theoretische Physik und Astrophysik, CAU Kiel, Leibnizstraße 15, 24098 Kiel

For the description of many–particle systems the Green’s function method has become widely used in the last decades. In this formalism the Kadanoff–Baym equation is solved using an appropriate self–energy. Additionaly the Generalized Kadanoff–Baym ansatz[1] (GKBA) is introduced to reconstruct the double–time single–particle Green’s function from its time–diagonal value: G(t₁,t₂)=F_GKBA[G(t₁=t₂)]. This approximation is well tested for large, homogeneous systems.

In this contribution, we apply the proposed scheme to finite model systems with strong spatial inhomogeneities: a Hubbard model, a 4–electron quantum dot[2] and a one–dimensional helium model. By comparing with results obtained from exact diagonalization, solutions of the time–dependent Schrödinger equation[3], Hartree–Fock– and full double–time Green’s function calculations[4], we test the validity of the approximation used.

[1] P. Lipavsky, V. Spicka, and B.Velicky, Phys. Rev. B 34, 6933–6942 (1986), [2] for comparison see poster by K. Balzer, [3] K. Balzer, S. Bauch, and M. Bonitz, Phys. Rev. A 81, 022510 (2010), [4] K. Balzer, S. Bauch, and M. Bonitz, Phys. Rev. A 82, 033427 (2010)