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Jussi Behrndt: The Landau Hamiltonian with delta-potentials supported on curves

Time: Fri 2023-03-31 11.00 - 12.00

Location: Kovalevskyrummet, Albano

Participating: Jussi Behrndt (TU Graz)

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The spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian \(A_\alpha =(i\nabla + \mathbf A)^2 + \alpha\delta_\Sigma\) in \(L^2(\mathbb R^2)\) with a \(\delta\)-potential supported on a finite \(C^{1,1}\)-smooth curve $\Sigma$ are studied. Here \(\mathbf A = \frac{1}{2} B (-x_2, x_1)^\top\) is the vector potential, B>0 is the strength of the homogeneous magnetic field, and \(\alpha\in L^\infty(\Sigma)\) is a position-dependent real coefficient modeling the strength of the singular interaction on the curve \(\Sigma\). After a general discussion of the qualitative spectral properties of \(A_\alpha\) and its resolvent, one of our main objectives is a local spectral analysis of \(A_\alpha\) near the Landau levels \(B(2q+1),\, q\in\mathbb N_0\).

This talk is based on joint works with P. Exner, M. Holzmann, V. Lotoreichik, and G. Raikov