The Spectral Shift Function and The Friedel Sum Rule
Mathematical Physics
2012-11-12 v2 Other Condensed Matter
math.MP
Abstract
We study the relationship between the spectral shift function and the excess charge in potential scattering theory. Although these quantities are closely related to each other, they have been often formulated in different settings so far. Here we first give an alternative construction of the spectral shift function, and then we prove that the spectral shift function thus constructed yields the Friedel sum rule.
Keywords
Cite
@article{arxiv.1111.5939,
title = {The Spectral Shift Function and The Friedel Sum Rule},
author = {Mahito Kohmoto and Tohru Koma and Shu Nakamura},
journal= {arXiv preprint arXiv:1111.5939},
year = {2012}
}
Comments
10 pages, no figure: The paper split into two parts. This is Part I which will appear in Annales Henri Poincare