Unitarity-Cuts and Berry’s Phase

Elaborating on the observation that two-particle unitarity-cuts of scattering amplitudes can be computed by applying Stokes’ theorem, we relate the optical theorem to the Berry phase, showing how the imaginary part of arbitrary one-loop Feynman amplitudes can be interpreted as the flux of a complex 2-form.     

The Dirichlet problem for the Laplace equation in a starlike domain of a Riemann surface

We consider the Dirichlet problem for the Laplace equation in a starlike domain, i.e. a domain which is normal with respect to a suitable polar co-ordinates system. Such a domain can be interpreted as a non-isotropically stretched unit circle. We write down the explicit solution in terms of a Fourier series whose coefficients are determined by solving an infinite system of linear equations depending on the boundary data. Numerical experiments show that the same method works even if the considered starlike domain belongs to a two-fold Riemann surface.     

Double-cut of scattering amplitudes and Stokes' Theorem

We show how Stokes' Theorem, in the fashion of the Generalised Cauchy Formula, can be applied for computing double-cut integrals of one-loop amplitudes analytically. It implies the evaluation of phase-space integrals of rational functions in two complex-conjugated variables, which are simply computed by an indefinite integration in a single variable, followed by Cauchy's Residue integration in the conjugated one. The method is suitable for the cut-construction of the coefficients of 2-point functions entering the decomposition of one-loop amplitudes in terms of scalar master integrals.     

Sharp non-resonance conditions for periodically perturbed Liénard systems

Archiv der Mathematik -     

Quantitative prediction of protein folding behaviors from a simple statistical model

The statistical nature of the protein folding process requires the use of equally detailed yet simple models that lend themselves to characterize experiments. One such model is the Wako-Saito?-Mun?oz-Eaton model, that we extend here to include solvation effects (WSME-S), introduced via empirical terms. We employ the novel version to analyze the folding of two proteins, gpW and SH3, that have similar size and thermodynamic stability but with the former folding 3 orders of magnitude faster than SH3. A quantitative analysis reveals that gpW presents at most marginal barriers, in contrast to SH3 that folds following a simple two-state approximation. We reproduce the observed experimental differences in melting temperature in gpW as seen by different experimental spectroscopic probes and the shape of the rate-temperature plot. In parallel, we predict the folding complexity expected in gpW from the analysis of both the residue-level thermodynamics and kinetics. SH3 serves as a stringent control with neither folding complexity nor dispersion in melting temperatures being observed. The extended model presented here serves as an ideal tool not only to characterize folding data but also to make experimentally testable predictions.     

Blue-shifting the monomer and excimer phosphorescence of tridentate cyclometallated platinum(II) complexes for optimal white-light OLEDs

By using a tridentate N^C^N-coordinating ligand, the luminescence of a cyclometallated Pt(II) complex can be shifted into the blue region, without the problematic drop-off in quantum yield observed for bidentate analogues. The combination of blue-shifted monomer and excimer allows white-emitting OLEDs with high colour rendering index to be produced.     

From red to near infra-red OLEDs: the remarkable effect of changing from X = -Cl to -NCS in a cyclometallated [Pt(N^C^N)X] complex {N^C^N = 5-mesityl-1,3-di-(2-pyridyl)benzene}

[PtL(6)X] {X = Cl or NCS and L(6) = 5-mesityl-1,3-di(2-pyridyl)-benzene} display similar luminescence in solution but, in the solid state, the packing of the molecules is different, with short PtPt interactions for X = NCS, leading to a red-shifted emission band. The effect has been used to generate OLEDs that emit squarely in the NIR region (855 nm).