Adiabatic approximation in time-dependent reduced-density-matrix functional theory
- Theoretische Festkoerperphysik, Universitaet Erlangen-Nuernberg, Staudtstrasse 7-B2, D-91058 Erlangen (Germany)
With the aim of describing real-time electron dynamics, we introduce an adiabatic approximation for the equation of motion of the one-body reduced density matrix (one-matrix). The eigenvalues of the one-matrix, which represent the occupation numbers of single-particle orbitals, are obtained from the constrained minimization of the instantaneous ground-state energy functional rather than from their dynamical equations. The performance of the approximation vis-a-vis nonadiabatic effects is assessed in real-time simulations of a two-site Hubbard model. Due to Landau-Zener-type transitions, the system evolves into a nonstationary state with persistent oscillations in the observables. The amplitude of the oscillations displays a strongly nonmonotonic dependence on the strength of the electron-electron interaction and the rate of variation of the external potential. We interpret an associated resonance behavior in the phase of the oscillations in terms of 'scattering' with spectator energy levels. To clarify the motivation for the minimization condition, we derive a sequence of energy functionals E{sub v}{sup (n)}, for which the corresponding sequence of minimizing one-matrices is asymptotic to the exact one-matrix in the adiabatic limit.
- OSTI ID:
- 21431018
- Journal Information:
- Physical Review. A, Vol. 81, Issue 4; Other Information: DOI: 10.1103/PhysRevA.81.042519; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
SUPERCONDUCTIVITY AND SUPERFLUIDITY
74 ATOMIC AND MOLECULAR PHYSICS
ADIABATIC APPROXIMATION
AMPLITUDES
ASYMPTOTIC SOLUTIONS
DENSITY MATRIX
EIGENVALUES
ELECTRON-ELECTRON COLLISIONS
ELECTRON-ELECTRON COUPLING
ELECTRON-ELECTRON INTERACTIONS
ELECTRONS
EQUATIONS OF MOTION
FUNCTIONALS
GROUND STATES
HUBBARD MODEL
MINIMIZATION
OCCUPATIONS
OSCILLATIONS
PARTICLES
TIME DEPENDENCE
APPROXIMATIONS
CALCULATION METHODS
COLLISIONS
COUPLING
CRYSTAL MODELS
DIFFERENTIAL EQUATIONS
ELECTRON COLLISIONS
ELEMENTARY PARTICLES
ENERGY LEVELS
EQUATIONS
FERMIONS
FUNCTIONS
INTERACTIONS
LEPTON-LEPTON INTERACTIONS
LEPTONS
MATHEMATICAL MODELS
MATHEMATICAL SOLUTIONS
MATRICES
OPTIMIZATION
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE INTERACTIONS