Generalization to higher dimensions of one-dimensional differential equation for Slater sum of an inhomogeneous electron liquid for a given local potential

Authors: Holas, A.¹; March, N. H.²

Source: Physics and Chemistry of Liquids, Volume 44, Number 4, August 2006 , pp. 465-475(11)

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Abstract:

The Slater sum (r, β) is the diagonal element of the canonical or Bloch density matrix, and by spatial integration yields the partition function. In one dimension, for independent electrons moving in a common potential v ( x ), the work of March and Murray ( Phys. Rev. , 120, 831 (1960)) already yielded a third-order partial differential equation for S ( x , β). But to date, a generalization to higher dimensions for independent electrons in a given v (r) has not been effected. Here, using the differential virial equation (Holas and March, Phys. Rev. A , 51, 2040 (1995)) such generalization is derived. As a special case, the known differential equation for S ( r , β) for three-dimensional spherically symmetric harmonic confinement is recovered. This equation is shown to be valid also for a wider, specific class of three-dimensional spherical systems.

Keywords: Inhomogeneous electron liquid; Slater sum; Harmonic confinement

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00319100500412287

Affiliations: 1: Institute of Physical Chemistry of the Polish Academy of Sciences, 44/52 Kasprzaka, 01-224 Warsaw, Poland 2: Oxford University, Oxford, England, UK

Publication date: 2006-08-01