Wannier Functions for Quasiperiodic Finite-Gap Potentials |
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Authors: | E D Belokolos V Z Enolskii M Salerno |
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Institution: | (1) Institute of Magnetism, Vernadski St. 36, Kiev-142, Ukraine;(2) Department of Mathematics and Statistics, Concordia University, 7141 Sherbrooke West, Montreal, H4B 1R6, Quebec, Canada;(3) Dipartimento di Fisica e Istituto Nazionale di Fisica della Materia (INFM), via S. Allende, I84081 Baronissi (SA), Italy |
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Abstract: | We consider Wannier functions of quasiperiodic g-gap (g ≥ 1) 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 σ-functions. Using this approach, we derive
a power series for the Wannier function for quasiperiodic potentials valid for |x| ≃ 0 and an asymptotic expansion valid at
large distances. These functions are important in a number of applied problems.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 234–256, August, 2005. |
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Keywords: | Wannier functions finite-gap potentials theta functions hyperelliptic curves |
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