Parnovski, L;
Shterenberg, R;
(2017)
Perturbation theory for spectral gap edges of 2D periodic Schrodinger operators.
Journal of Functional Analysis
, 273
(1)
pp. 444-470.
10.1016/j.jfa.2017.02.030.
Preview |
Text
Parnovski_perturbation theory for_2D.pdf - Published Version Download (510kB) | Preview |
Abstract
We consider a two-dimensional periodic Schrödinger operator H=−Δ+W with Γ being the lattice of periods. We investigate the structure of the edges of open gaps in the spectrum of H. We show that under arbitrary small perturbation V periodic with respect to N Γ where N=N(W) is some integer, all edges of the gaps in the spectrum of H+V which are perturbation of the gaps of H become non-degenerate, i.e. are attained at finitely many points by one band function only and have non-degenerate quadratic minimum/maximum. We also discuss this problem in the discrete setting and show that changing the lattice of periods may indeed be unavoidable to achieve the non-degeneracy.
| Type: | Article |
|---|---|
| Title: | Perturbation theory for spectral gap edges of 2D periodic Schrodinger operators |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.jfa.2017.02.030 |
| Publisher version: | http://doi.org/10.1016/j.jfa.2017.02.030 |
| Language: | English |
| Additional information: | This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
| Keywords: | Science & Technology, Physical Sciences, Mathematics, Periodic operators, Band functions, Bloch surfaces |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1554799 |
Archive Staff Only
 |
View Item |
