Complex periodic potentials with real band spectra
Condensed Matter
2011-03-23 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
This paper demonstrates that complex PT-symmetric periodic potentials possess real band spectra. However, there are significant qualitative differences in the band structure for these potentials when compared with conventional real periodic potentials. For example, while the potentials V(x)=i\sin^{2N+1}(x), (N=0, 1, 2, ...), have infinitely many gaps, at the band edges there are periodic wave functions but no antiperiodic wave functions. Numerical analysis and higher-order WKB techniques are used to establish these results.
Cite
@article{arxiv.cond-mat/9810369,
title = {Complex periodic potentials with real band spectra},
author = {Carl M. Bender and Gerald V. Dunne and Peter N. Meisinger},
journal= {arXiv preprint arXiv:cond-mat/9810369},
year = {2011}
}
Comments
8 pages, 7 figures, LaTeX