Geodesic
Wannier Functions for Quasiperiodic Finite-Gap Potentials
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 2, pp. 234-256

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We consider Wannier functions of quasiperiodic $g$-gap ($g\geq1$) potentials and investigate their main properties. In particular, we discuss the problem of averaging that underlies the definition of the Wannier functions for both periodic and quasiperiodic potentials and express Bloch functions and quasimomenta in terms of hyperelliptic $\sigma$-functions. Using this approach, we derive a power series for the Wannier function for quasiperiodic potentials valid for $|x|\simeq0$, and an asymptotic expansion valid at large distances. These functions are important in a number of applied problems.
Keywords: Wannier functions, finite-gap potentials, theta functions, hyperelliptic curves. 
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     author = {E. D. Belokolos and V. Z. \`Enol'skii and M. Salerno},
     title = {Wannier {Functions} for {Quasiperiodic} {Finite-Gap} {Potentials}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {234--256},
     publisher = {mathdoc},
     volume = {144},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_144_2_a2/}
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E. D. Belokolos; V. Z. Ènol'skii; M. Salerno. Wannier Functions for Quasiperiodic Finite-Gap Potentials. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 2, pp. 234-256. http://geodesic.mathdoc.fr/item/TMF_2005_144_2_a2/