Localization properties and wavelet-like orthonormal basesfor the lowest Landau level
(2001) Advances in Gabor Analysis — ISBN: [978-0-8176-4239-6], p. 223-258, published
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- Authors
Antoine, Jean-Pierre 
- Abstract
- As an illustration of the phase space localization problem of quantum mechanical systems, we study a two-dimensional electron gas in a magnetic field, such as encountered in the Fractional Quantum Hall Effect (FQHE). We discuss a general procedure for constructing an orthonormal basis for the lowest Landau level (as well as for the other Landau levels), starting from an arbitrary orthonormal basis in L^2(R). After some remarks concerning localization properties of the wave functions of any orthonormal basis in the Landau levels, we discuss in detail some relevant examples stemming from wavelet analysis like the Haar, the Littlewood-Paley, the Journé and the splines bases. We also propose a toymodel, which indicates how the use of wavelets in the analysis of the FQHE may help in the search of the correct ground state of the system. Finally, we exhibit an intriguing equivalence between FQHE states generated by the so-called magnetic translations and vectors of an orthonormal basis derived from an arbitrary multiresolution analysis.
- Affiliations
Università di Palermo Dipartimento di Matematica ed Applicazioni, Facoltà di Ingegneria
Citations
Antoine, J.-P., & Bagarello, F. (2001). Localization properties and wavelet-like orthonormal basesfor the lowest Landau level. In H.G.Feichtinger and T.Strohmer (eds.) (ed.), Advances in Gabor Analysis (p. p. 223-258). Birkhäuser. https://hdl.handle.net/2078.5/24870