Berlin 2014 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 13: Poster (permanent Mo-Do)

MP 13.6: Poster

Tuesday, March 18, 2014, 08:00–18:00, SPA Foyer

Distribution of the Proper Delay Times of an Andreev Quantum Dot — •Jonas Lammers¹, Francesco Mezzadri², and Reinhard F. Werner¹ — ¹Institut für Theoretische Physik, Leibniz Universität Hannover — ²School of Mathematics, University of Bristol, UK

Andreev Quantum Dots (QDs) are mesoscopic conductors in contact with superconductors which allow for phase-coherent transport of individual electrons and whose intrinsic classical dynamics is fully chaotic (disordered conductor). Instead of trying to predict the behavior of an individual dot it is sensible to treat QDs as stochastic entities, using Random Matrix Theory (RMT) to obtain the statistics of their properties. One of the transport properties of interest is the time delay suffered by incoming particles due to the complex dynamics inside. This is intimately related to the Wigner-Smith time delay matrix Q=−iℏ S^†(∂ S/∂ E), which is determined by the energy-derivative of the system’s unitary scattering matrix S(E). More specifically we are interested in the distribution of the eigenvalues of Q, known as Proper Delay Times (PDTs). Their average gives the Wigner Time Delay, the average time a particle spends inside the QD, and they can be used to determine a number of other quantities beyond the time delay problem.

We compute the distribution P(τ₁,…,τ_N) of the PDTs of Andreev QDs for all four Altland-Zirnbauer random matrix symmetry classes, D, DIII, C, and CI, depending on the presence/absence of time-reversal invariance and/or spin-rotation symmetry.