Multi-loop Integrand Reduction with Computational Algebraic Geometry

We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general parameterisation of any multi-loop integrand in a renormalizable gauge theory. The method relies on computational algebraic geometry techniques such as Gr\"obner bases and primary decomposition of ideals. We present some results for two and three loop amplitudes obtained with the help of the Macaulay2 computer algebra system and the Mathematica package BasisDet.Comment: Contribution to the 15th International Workshop on advanced computing and analysis techniques (ACAT 2013), 16-21 May, Beijing, China. 8 pages, 2 figure

Multi-loop integrand reduction techniques

We review recent progress in D-dimensional integrand reduction algorithms for two loop amplitudes and give examples of their application to non-planar maximal cuts of the five-point all-plus helicity amplitude in QCD.Comment: 8 pages, Contribution to the proceedings of Loops and Legs in Quantum Field Theory, 27 April - 2 May 2014, Weimar, German

Theory of Electron-Phonon Dynamics in Insulating Nanoparticles

We discuss the rich vibrational dynamics of nanometer-scale semiconducting and insulating crystals as probed by localized electronic impurity states, with an emphasis on nanoparticles that are only weakly coupled to their environment. Two principal regimes of electron-phonon dynamics are distinguished, and a brief survey of vibrational-mode broadening mechanisms is presented. Recent work on the effects of mechanical interaction with the environment is discussed.Comment: Revte