Well-behaved coarse-grained model of density-functional theory

作者：Lammert Paul E^*

来源：Physical Review A, 2010, 82(1): 012109.

DOI：10.1103/PhysRevA.82.012109

A coarse-grained version of quantum density-functional theory featuring a limited spatial resolution is shown to model formal density-functional theory (DFT). This means that all densities are ensemble-V-representable (that is, by mixed states), the intrinsic energy functional F is a continuous function of the density, and the representing external potential is the functional derivative of the intrinsic energy, in the sense of directional derivatives within the domain of F. The representing potential upsilon[rho] also has a quasicontinuity property, specifically, upsilon[rho]rho is continuous as a function of rho. Convergence of the intrinsic energy, coarse-grained densities, and representing potentials in the limit of coarse-graining scale going to zero are studied vis-a-vis Lieb's L-1 boolean AND L-3 theory. The intrinsic energy converges monotonically to its fine-grained (continuum) value, and coarse-grainings of a density rho converge strongly to rho. If a sequence of coarse-grained densities converges strongly to rho and their representing potentials converge weak-*, the limit is the representing potential for rho. Conversely, L-3/2 + L-infinity representability implies the existence of such a coarse-grained sequence.

• 出版日期2010-7-23