TY - JOUR

T1 - Vortex structure and characterization of quasiperiodic functions

AU - Dana, Itzhack

AU - Chernov, Vladislav E.

PY - 2002/11/29

Y1 - 2002/11/29

N2 - Quasiperiodic functions (QPFs) are characterized by their full vortex structure in one unit cell. This characterization is much finer and more sensitive than the topological one given by the total vorticity per unit cell (the 'Chern index'). It is shown that QPFs with an arbitrarily prescribed vortex structure exist by constructing explicitly such a 'standard' QPF. Two QPFs with the same vortex structure are equivalent, in the sense that their ratio is a function which is strictly periodic, nonvanishing and at least continuous. A general QPF can then be approximately reconstructed from its vortex structure on the basis of the standard QPF and the equivalence concept. As another application of this concept, a simple method is proposed for calculating the quasiperiodic eigenvectors of periodic matrices. Possible applications to the quantum-chaos problem on a phase-space torus are briefly discussed.

AB - Quasiperiodic functions (QPFs) are characterized by their full vortex structure in one unit cell. This characterization is much finer and more sensitive than the topological one given by the total vorticity per unit cell (the 'Chern index'). It is shown that QPFs with an arbitrarily prescribed vortex structure exist by constructing explicitly such a 'standard' QPF. Two QPFs with the same vortex structure are equivalent, in the sense that their ratio is a function which is strictly periodic, nonvanishing and at least continuous. A general QPF can then be approximately reconstructed from its vortex structure on the basis of the standard QPF and the equivalence concept. As another application of this concept, a simple method is proposed for calculating the quasiperiodic eigenvectors of periodic matrices. Possible applications to the quantum-chaos problem on a phase-space torus are briefly discussed.

UR - http://www.scopus.com/inward/record.url?scp=0037195745&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/35/47/310

DO - 10.1088/0305-4470/35/47/310

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AN - SCOPUS:0037195745

SN - 0305-4470

VL - 35

SP - 10101

EP - 10116

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 47

ER -