On some mathematical identities resulting from evaluation of the partition function for an electron moving in a periodic lattice

Abstract

We consider a simple model of the dynamics of a single electron in a crystal lattice. Although this is a standard problem in condensed matter physics, alternative ways of evaluating a partition function for such a system lead to equalities, that may be interesting from the point of view of mathematical analysis, combinatorics and graph theory.

arXiv comment27 pages