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TMF, 2005, Volume 144, Number 2, Pages 234–256 (Mi tmf1850)  

This article is cited in 4 scientific papers (total in 4 papers)

Wannier Functions for Quasiperiodic Finite-Gap Potentials

E. D. Belokolosa, V. Z. Ènol'skiib, M. Salernoc

a Institute of Magnetism, National Academy of Sciences of Ukraine
b Concordia University, Department of Mathematics and Statistics
c INFM — Istituto Nazionale di Fisica della Materia

Abstract: 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

DOI: https://doi.org/10.4213/tmf1850

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English version:
Theoretical and Mathematical Physics, 2005, 144:2, 1081–1099

Bibliographic databases:


Citation: E. D. Belokolos, V. Z. Ènol'skii, M. Salerno, “Wannier Functions for Quasiperiodic Finite-Gap Potentials”, TMF, 144:2 (2005), 234–256; Theoret. and Math. Phys., 144:2 (2005), 1081–1099

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Grosset M.-P., Veselov A.P., “Elliptic Faulhaber polynomials and Lame densities of states”, International Mathematics Research Notices, 2006, 62120  mathscinet  zmath  isi
    2. Vega G.T., “Some nonlinear solutions of the linear Schrodinger equation for a free particle”, Advanced Summer School in Physics 2006 - FRONTIERS IN CONTEMPORARY PHYSICS, AIP Conference Proceedings, 885, 2007, 34–39  crossref  adsnasa  isi  scopus  scopus
    3. Eilbeck, JC, “Addition formulae over the Jacobian pre-image of hyperelliptic Wirtinger varieties”, Journal fur Die Reine und Angewandte Mathematik, 619 (2008), 37  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Kodama Yu., Matsutani Sh., Previato E., “Quasi-Periodic and Periodic Solutions of the Toda Lattice via the Hyperelliptic SIGMA Function”, Ann. Inst. Fourier, 63:2 (2013), 655–688  crossref  mathscinet  zmath  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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