Friedel Sum Rule as a Trace Formula

Details Friedel Sum Rule as a Trace Formula Friedel Sum Rule as a Trace Formula

2005-08-15

arxiv.org/abs/math-ph/0508030v2

Physics

Mathematical Physics

12 pages, no figures, v2: major revision, the argument about the integrality of the excess charge deleted, title changed

Scientific paper

We examine the Friedel sum rule which states that the "excess charge" due to a single impurity potential in a metal is equal to a sum of phase shifts for scatterings of electrons by the impurity. For finite volume, the ``excess charge" is given by the difference between total numbers of levels in the Fermi sea with and without the impurity potential. However, a sequence of the "excess charge" for finite volume is not necessarily bounded in the infinite volume limit, as was pointed out by Kirsch. In order to circumvent this difficulty, we define "excess charge" directly for the infinite volume. The Friedel sum rule is proven to hold for the "excess charge" thus defined.

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