Analytic Dirac approximation for real linear algebraic groups

For a real linear algebraic group G let A(G) be the algebra of analytic vectors for the left regular representation of G on the space of superexponentially decreasing functions. We present an explicit Dirac sequence in A(G). Since A(G) acts on E for every Frechet-representation (\pi,E) of moderate growth, this yields an elementary proof of a result of Nelson that the space of analytic vectors is dense in E.Comment: 7 page

Aspects of analytic representation theory

[no abstract

Exponential Decay Lifetimes of Excitons in Individual Single-Walled Carbon Nanotubes

The dynamics of excitons in individual semiconducting single-walled carbon nanotubes was studied using time-resolved photoluminescence (PL) spectroscopy. The PL decay from tubes of the same (n,m) type was found to be monoexponential, however, with lifetimes varying between less than 20 and 200 ps from tube to tube. Competition of nonradiative decay of excitons is facilitated by a thermally activated process, most likely a transition to a low-lying optically inactive trap state that is promoted by a low-frequency phonon mode

Two-dimensional electronic spectroscopy from first principles

The development of multidimensional, ultrafast spectroscopy techniques calls for the development of efficient computational schemes that allow for the simulation of such experiments and thus for the interpretation of the corresponding results. In this work, we present the development of a fully first-principles scheme to compute two-dimensional electron spectroscopy maps based on real-time time-dependent density-functional theory. The interface of this approach with the Ehrenfest scheme for molecular dynamics enables the inclusion of vibronic effects in the calculations. We demonstrate the effectiveness of this method by applying it to prototypical molecules such as benzene, pyridine, and pyrene. We discuss the role of the approximations that inevitably enter the adopted theoretical framework and set the stage for further extensions of the proposed method

Strongly coupled, high-quality plasmonic dimer antennas fabricated using a sketch-and-peel technique

A combination of helium- and gallium-ion beam milling together with a fast and reliable sketch-and-peel technique is used to fabricate gold nanorod dimer antennas with an excellent quality factor and with gap distances of less than 6 nm. The high fabrication quality of the sketch-and-peel technique compared to a conventional ion beam milling technique is proven by polarisation-resolved linear dark-field spectromicroscopy of isolated dimer antennas. We demonstrate a strong coupling of the two antenna arms for both fabrication techniques, with a quality factor of more than 14, close to the theoretical limit, for the sketch-and-peel-produced antennas compared to only 6 for the conventional fabrication process. The obtained results on the strong coupling of the plasmonic dimer antennas are supported by finite-difference time-domain simulations of the light-dimer antenna interaction. The presented fabrication technique enables the rapid fabrication of large-scale plasmonic or dielectric nanostructures arrays and metasurfaces with single-digit nanometer scale milling accuracy. © 2020 Christoph Lienau, Martin Silies et al., published by De Gruyter, Berlin/Boston