Wednesday, January 23, 2013

1301.5169 (Diomba Sambou)

Lieb-Thirring type inequalities for non-selfadjoint perturbations of
magnetic Schrödinger operators

Diomba Sambou
Let $H := H_{0} + V$ and $H_{\perp} := H_{0,\perp} + V$ be respectively perturbations of the free Schr\"odinger operators $H_{0}$ on $L^{2}\big(\mathbb{R}^{2d+1}\big)$ and $H_{0,\perp}$ on $L^{2}\big(\mathbb{R}^{2d}\big)$, $d \geq 1$ with constant magnetic field of strength $b>0$, and $V$ is a complex relatively compact perturbation. We prove Lieb-Thirring type inequalities for the discrete spectrum of $H$ and $H_{\perp}$. In particular, these estimates give $a\, priori$ information on the distribution of eigenvalues around the Landau levels of the operator, and describe how fast sequences of eigenvalues converge.
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