Time-dependent occupation numbers in reduced-density-matrix functional theory: Application to an interacting Landau-Zener model

Details Time-dependent occupation numbers in reduced-density-matrix functional theory: Application to an interacting Landau-Zener model Time-dependent occupation numbers in reduced-density-matrix functional theory: Application to an interacting Landau-Zener model

2010-11-04

arxiv.org/abs/1011.1220v3

Phys. Rev. A, vol. 83, 052510 (2011)

Physics

Condensed Matter

Strongly Correlated Electrons

6 pages, revised, Fig. 2 added

Scientific paper

We prove that if the two-body terms in the equation of motion for the one-body reduced density matrix are approximated by ground-state functionals, the eigenvalues of the one-body reduced density matrix (occupation numbers) remain constant in time. This deficiency is related to the inability of such an approximation to account for relative phases in the two-body reduced density matrix. We derive an exact differential equation giving the functional dependence of these phases in an interacting Landau-Zener model and study their behavior in short- and long-time regimes. The phases undergo resonances whenever the occupation numbers approach the boundaries of the interval [0,1]. In the long-time regime, the occupation numbers display correlation-induced oscillations and the memory dependence of the functionals assumes a simple form.

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