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

Journal Article · Sun May 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.052510· OSTI ID:21546759

Requist, Ryan; Pankratov, Oleg ^[1]

---

1. Theoretische Festkoerperphysik, Universitaet Erlangen-Nuernberg, Staudtstrasse 7-B2, D-91058 Erlangen (Germany)

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.

• OSTI ID: 21546759
• Journal Information: Physical Review. A, Vol. 83, Issue 5; Other Information: DOI: 10.1103/PhysRevA.83.052510; (c) 2011 American Institute of Physics; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
APPROXIMATIONS
CORRELATIONS
DENSITY MATRIX
EIGENVALUES
EQUATIONS OF MOTION
FUNCTIONALS
LANDAU-ZENER FORMULA
OSCILLATIONS
RESONANCE
TIME DEPENDENCE
TWO-BODY PROBLEM
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
MANY-BODY PROBLEM
MATRICES
PARTIAL DIFFERENTIAL EQUATIONS