Wannier functions for quasi-periodic finite-gap potentials

Details Wannier functions for quasi-periodic finite-gap potentials Wannier functions for quasi-periodic finite-gap potentials

2004-12-22

arxiv.org/abs/math-ph/0412081v1

Physics

Mathematical Physics

Scientific paper

10.1007/s11232-005-0138-2

In this paper we consider Wannier functions of quasi-periodic g-gap ($g\geq 1$) potentials and investigate their main properties. In particular, we discuss the problem of averaging underlying the definition of Wannier functions for both periodic and quasi-periodic potentials and express Bloch functions and quasi-momenta in terms of hyperelliptic $\sigma$ functions. Using this approach we derive a power series expansion of the Wannier function for quasi-periodic potentials valid at $|x|\simeq 0$ and an asymptotic expansion valid at large distance. These functions are important for a number of applied problems.

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