arXiv subjects
Publications and source records attributed to Nour Kerraoui.
We investigate the inverse problem of retrieving the magnetic potential of an Iwatsuka Hamiltonian through knowledge of its first band function. We prove that two magnetic potentials sharing the same first band function not just between them, but between all fields within the family linearly interpolating between them and accumulating at one end point, coincide.
In this paper we investigate the spectrum of the Dirac operator posed in a tubular neighborhood of a planar loop with infinite mass boundary conditions. We show that when thewidth of the tubular neighborhood goes to zero the asymptotic expansion of the eigenvalues isdriven by a one dimensional operator of geometric nature involving the curvature of the loop.
We consider the two-dimensional Dirac operator with infinite mass boundary conditions posed in a tubular neighborhood of a $C^4$-planar curve. Under generic assumptions on its curvature $κ$, we prove that in the thin-width regime the splitting of the eigenvalues is driven by the one dimensional Schrödinger operator on $L^2(\mathbb R)$ \[ \mathcal{L}_e := -\frac{d^2}{ds^2} - \frac{κ^2}{π^2} \] with a geometrically induced potential. The eigenvalues are shown to be at distance of order $\varepsilon$ from the essential spectrum, where $2\varepsilon$ is the width of the waveguide. This is in contrast with the non-relativistic counterpart of this model, for which they are known to be at a finite distance.