Bloch equation for the canonical density matrix in terms of its diagonal element: the Slater sumBloch equation for the canonical density matrix in terms of its diagonal element: the Slater sum
Faculty of Sciences. Physics

Department of Physics

article

2009Amsterdam, 2009

Physics

Physics letters: A. - Amsterdam, 1967, currens

373(2009):18/19, p. 1691-1692

0375-9601

000269486700019

E

English (eng)

University of Antwerp

In early work, March and Murray (MM) solved the Bloch equation for the canonical density matrix generated by a given potential V(r) using perturbation theory to all orders in V, the unperturbed problem being that of free homogeneous electrons. Here, we avoid perturbation theory by using, but now in one dimension, the MM differential equation for the so-called Slater sum S(x,À) for given V(x), to write the Bloch equation for C(x,x,À) in terms of its diagonal element C(x,x,À)|x=x=S(x,À), where À=(kBT)−1. In the language of the Feynman propagator, À¨it where t is the time, and this propagator is then characterized solely by its diagonal element in one dimension. The connection with ground-state density functional theory is finally emphasized.

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