Density functional formalism in the canonical ensemble

Details Density functional formalism in the canonical ensemble Density functional formalism in the canonical ensemble

2000-08-19

arxiv.org/abs/cond-mat/0008291v1

Physics

Condensed Matter

Statistical Mechanics

revtex, to be submitted to Phys. Rev. Lett

Scientific paper

10.1088/0953-8984/13/25/101

Density functional theory, when applied to systems with $T\neq 0$, is based on the grand canonical extension of the Hohenberg-Kohn-Sham theorem due to Mermin (HKSM theorem). While a straightforward canonical ensemble generalization fails, work in nanopore systems could certainly benefit from such extension. We show that, if the asymptotic behaviour of the canonical distribution functions is taken into account, the HKSM theorem can be extended to the canonical ensemble. We generate $N$-modified correlation and distribution functions hierarchies and prove that, if they are employed, either a modified external field or the density profiles can be indistinctly used as independent variables. We also write down the $N$% -modified free energy functional and prove that its minimum is reached when the equilibrium values of the new hierarchy are used. This completes the extension of the HKSM theorem.

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