Dresden 2009 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 21: Quantum chaos II

DY 21.1: Talk

Thursday, March 26, 2009, 10:15–10:30, ZEU 255

The x-ray edge problem in integrable quantum dots — •Georg Röder and Martina Hentschel — Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany

The x-ray edge problem in metals, which constitutes a well-studied many-body problem, is a classic problem in condensed matter physics. Here we address the question how the smallness and the individual properties of mesoscopic systems such as quantum dots affect the Fermi-edge singularities in the photo absorption signal. To this end, we follow a Fermi golden rule approach and model the localized core hole left behind upon the excitation of a core electron as a localized, or rank one, perturbation [K.Ohtaka and Y.Tanabe, RMP 62, 929 (1990)]. For the transition of a s core electron into a s-like quantum dot level (K-edge), we find the threshold absorption processes to be enhanced compared to the metallic case where typically a rounded K-edge is found as a consequence of Anderson orthogonality catastrophe. The enhancement is particularly strong when the core hole appears close to the (hard-wall) boundary of quantum dots of integrable (circular and rectangular) shape. This effect holds also for parabolic quantum dots that possess soft walls. An external magnetic field further increases the peaked photo absorption signal at the K-edge. We compare our findings to results for chaotic quantum dots obtained by random matrix theory [M.Hentschel, D.Ullmo and H.Baranger, PRL 93, 176807 (2004)].