TY - JOUR

T1 - N-representability and stationarity in time-dependent density-functional theory

AU - Cohen, Morrel H.

AU - Wasserman, Adam

PY - 2005/3/1

Y1 - 2005/3/1

N2 - To construct an N-representable time-dependent density-functional theory, a generalization to the time domain of the Levy-Lieb (LL) constrained-search algorithm is required. That the action is only stationary in the Dirac-Frenkel variational principle eliminates the possibility of basing the search on the action itself. Instead, we use the norm of the partial functional derivative of the action in the Hilbert space of the wave functions in place of the energy of the LL search. The electron densities entering the formalism are N-representable, and the resulting universal action functional has a unique stationary point in the density at that corresponding to the solution of the Schrödinger equation. The original Runge-Gross (RG) formulation is subsumed within the current formalism. Concerns in the literature about the meaning of the functional derivatives and the internal consistency of the RG formulation are allayed by clarifying the nature of the functional derivatives entering the formalism.

AB - To construct an N-representable time-dependent density-functional theory, a generalization to the time domain of the Levy-Lieb (LL) constrained-search algorithm is required. That the action is only stationary in the Dirac-Frenkel variational principle eliminates the possibility of basing the search on the action itself. Instead, we use the norm of the partial functional derivative of the action in the Hilbert space of the wave functions in place of the energy of the LL search. The electron densities entering the formalism are N-representable, and the resulting universal action functional has a unique stationary point in the density at that corresponding to the solution of the Schrödinger equation. The original Runge-Gross (RG) formulation is subsumed within the current formalism. Concerns in the literature about the meaning of the functional derivatives and the internal consistency of the RG formulation are allayed by clarifying the nature of the functional derivatives entering the formalism.

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U2 - 10.1103/PhysRevA.71.032515

DO - 10.1103/PhysRevA.71.032515

M3 - Article

AN - SCOPUS:18544379309

SN - 1050-2947

VL - 71

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 3

M1 - 032515

ER -