Classical path approximation for one-electron Green's function in a magnetic field and the density functional model

This paper is an extension of our previous work on density functional models of electrons in magnetic fields. A full "classical path" (CP) one-body Green's function is used in the calculation of the kinetic functional and the one particle density. This treatment leads to a more precise expression of the density functional theory in the strong B case, in which magnetic fields are much stronger than the external scalar potential. In the semiclassical limit t → 0, the CP Green's function is checked by an exact solvable system, interactionless electrons in a central harmonic potential and a constant magnetic field. It turns out that the Green's function is correct through the order O(t²). Furthermore, in the high B limit (but still t→0), the leading terms in B of the CP Green's function are the same as those of the exact Green's function in the entire t-expansion series.