Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session C37: Undergraduate Research VI: Education Research and Related Studies
3:00 PM–5:00 PM,
Monday, March 15, 2021
Sponsoring
Unit:
APS/SPS
Chair: Olga Shishkov, University of Colorado, Boulder
Abstract: C37.00010 : Characterizing Time-Frequency Localization for Electronic-Wavefunction Basis Sets*
4:48 PM–5:00 PM
Live
Presenter:
Antonino Travia
(Univ of South Florida)
Authors:
Antonino Travia
(Univ of South Florida)
David Rabson
(Univ of South Florida)
the temporal (spatial) domain; meanwhile, the Fourier basis is completely
localized in the frequency (wavenumber) domain and completely delocalized in
time (space). In the last century, Haar, Daubechies and others introduced
basis sets between these extremes which are partially localized in each
domain. Although these new bases offer extensive freedom,
optimizing the choice of wavelet for a particular application
remains an open question. If one wanted to quantify how localized a single
wavelet is in each of these domains, the obvious thing would be to measure the
variance in the appropriate basis functions; however, this fails to
characterize a wavelet basis set as a whole. We provide
a quantitative measure for choosing a basis set by describing how close
it is to the Dirac basis, the Fourier basis, or in fact any
basis set, bounded by natural localization extrema. We discuss
an application to electronic wavefunctions on the Fibonacci chain.
*This material is based in part on work done by DAR while serving at the National Science Foundation. Any opinion, findings, conclusions, or recommendations expressed are those of the authors and do not necessarily reflect the views of the National Science Foundation.
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