Multi-Resolution Analysis and Fractional Quantum Hall Effect: an Equivalence Result
نویسنده
چکیده
In this paper we prove that any multi-resolution analysis of L2(R) produces, for some values of the filling factor, a single-electron wave function of the lowest Landau level (LLL) which, together with its (magnetic) translated, gives rise to an orthonormal set in the LLL. We also give the inverse construction. Moreover, we extend this procedure to the higher Landau levels and we discuss the analogies and the differences between this procedure and the one previously proposed by J.-P. Antoine and the author. PACS Numbers: 02.30.Nw, 73.43.f
منابع مشابه
Multi-Resolution Analysis and Fractional Quantum Hall Effect: More Results
In a previous paper we have proven that any multi-resolution analysis of L2(R) produces, for even values of the inverse filling factor and for a square lattice, a single-electron wave function of the lowest Landau level (LLL) which, together with its (magnetic) translated, gives rise to an orthonormal set in the LLL. We have also discussed the inverse construction. In this paper we simplify the...
متن کاملRelations between multi-resolution analysis and quantum mechanics
We discuss a procedure to construct multi-resolution analyses (MRA) of L2(R) starting from a given seed function h(s) which should satisfy some conditions. Our method, originally related to the quantum mechanical hamiltonian of the fractional quantum Hall effect (FQHE), is shown to be model independent. The role of a canonical map between certain canonically conjugate operators is discussed. Th...
متن کاملHausdorff dimension and anyonic distribution functions
We obtain the distribution functions for anyonic excitations classified into equivalence classes labeled by Hausdorff dimension, h and as an example of such anyonic systems, we consider the collective excitations of the Fractional Quantum Hall Effect ( FQHE ). PACS numbers: 05.30.-d, 05.70Ge
متن کاملar X iv : h ep - t h / 99 05 22 9 v 13 2 4 N ov 1 99 9 Fractons and Fractal Statistics ∗
Fractons are anyons classified into equivalence classes and they obey a specific fractal statistics. The equivalence classes are labeled by a fractal parameter or Hausdorff dimension h. We consider this approach in the context of the Fractional Quantum Hall Effect ( FQHE ) and the concept of duality between such classes, defined by h̃ = 3−h shows us that the filling factors for which the FQHE we...
متن کاملar X iv : h ep - t h / 99 05 22 9 v 11 1 5 N ov 1 99 9 Fractons and Fractal Statistics ∗
Fractons are anyons classified into equivalence classes and they obey a specific fractal statistics. The equivalence classes are labeled by a fractal parameter or Hausdorff dimension h. We consider this approach in the context of the Fractional Quantum Hall Effect ( FQHE ) and the concept of duality between such classes, defined by h̃ = 3−h shows us that the filling factors for which the FQHE we...
متن کامل