Title
Bloch equation for the canonical density matrix in terms of its diagonal element: the Slater sum Bloch equation for the canonical density matrix in terms of its diagonal element: the Slater sum
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
Amsterdam ,
Subject
Physics
Source (journal)
Physics letters: A. - Amsterdam, 1967, currens
Volume/pages
373(2009) :18/19 , p. 1691-1692
ISSN
0375-9601
ISI
000269486700019
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
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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