Laboratoire de Physique Théorique
Toulouse - UMR 5152

In this talk, I will present two different lines of work in the fields of condensed matter and chaotic quantum scattering :

The first part is about the manipulation and detection of excitations with unusual exchange statistics (non-Abelian anyons) in superconductors. We present an approach which allows to inject on demand so-called edge vortices in a topological superconductors. They are pi-phase domain walls which propagate along the chiral edge channels, and possess non-Abelian statistics. We show that the signatures of this unusual exchange statistics can be detected in an electrical measurement.

The second part is devoted to chaotic quantum scattering. The temporal aspects of a scattering process are encoded in the Wigner-Smith time delay matrix. Within the framework of random matrix theory, we obtain the distribution of the Wigner-Smith matrix for chaotic cavities in the presence of absorption. This is an extension of the celebrated Wishart-Laguerre distribution obtained in the absence of absorption by Brouwer, Frahm and Beenakker (1997-99). We show how this distribution can be interpreted in terms of two interacting 1D Coulomb gases.

Références :

1. Electrical detection of the Majorana fusion rule for chiral edge vortices in a topological superconductor : C.W.J Beenakker, A. Grabsch, Y. Herasymenko, SciPost Phys. 6, 022 (2019)

Time-resolved electrical detection of chiral edge vortex braiding : I. Adagideli, F. Hassler, A. Grabsch, M. Pacholski, C.W.J. Beenakker, arXiv:1907.02422

Distribution of the Wigner-Smith time-delay matrix for chaotic cavities with absorption and coupled Coulomb gases : A. Grabsch, arXiv:1909.01002