# Peierls' substitution for low lying spectral energy windows

@article{Cornean2017PeierlsSF, title={Peierls' substitution for low lying spectral energy windows}, author={Horia D. Cornean and Bernard Helffer and Radu Purice}, journal={Journal of Spectral Theory}, year={2017} }

We consider a $2d$ magnetic Schrodinger operator perturbed by a weak magnetic field which slowly varies around a positive mean. In a previous paper we proved the appearance of a `Landau type' structure of spectral islands at the bottom of the spectrum, under the hypothesis that the lowest Bloch eigenvalue of the unperturbed operator remained simple on the whole Brillouin zone, even though its range may overlap with the range of the second eigenvalue. We also assumed that the first Bloch…

## 4 Citations

### Spectral analysis near a Dirac type crossing in a weak non-constant magnetic field

- PhysicsTransactions of the American Mathematical Society
- 2021

This is the last paper in a series of three in which we have studied the Peierls substitution in the case of a weak magnetic field. Here we deal with two
2
d
2d
Bloch eigenvalues which…

### Magnetic pseudodifferential operators represented as generalized Hofstadter-like matrices

- MathematicsJournal of Pseudo-Differential Operators and Applications
- 2018

First, we reconsider the magnetic pseudodifferential calculus and show that for a large class of non-decaying symbols, their corresponding magnetic pseudodifferential operators can be represented, up…

### Magnetic pseudodifferential operators represented as generalized Hofstadter-like matrices

- MathematicsJournal of Pseudo-Differential Operators and Applications
- 2018

First, we reconsider the magnetic pseudodifferential calculus and show that for a large class of non-decaying symbols, their corresponding magnetic pseudodifferential operators can be represented, up…

### Characterization of edge states in perturbed honeycomb structures

- Physics, MathematicsPure and Applied Analysis
- 2019

This paper is a mathematical analysis of conduction effects at interfaces between insulators. Motivated by work of Haldane-Raghu , we continue the study of a linear PDE initiated in papers of…

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