The basin boundary of the breakup channel in chaotic rearrangement scattering

Nonlinear Dynamics - We present an example of demonstration for the basin boundaries in classical rearrangement scattering with particular emphasis on the breakup channel. Whereas the basin...     

Dynamical Gibbs–Non-Gibbs Transitions in Lattice Widom–Rowlinson Models with Hard-Core and Soft-Core Interactions

Journal of Statistical Physics - We consider the Widom–Rowlinson model on the lattice $${\mathbb {Z}}^d$$ in two versions, comparing the cases of a hard-core repulsion and of a soft-core...     

Functionalization of silicon nanoparticles via hydrosilylation with 1-alkenes

Studies focusing on the functionalization of the surface of free silicon nanoparticles are presented. This functionalization is applied to hydrogen-terminated silicon nanoparticles to evaluate how far the well-known solution-phase chemistry of thermal-, radical-, Lewis acid- and UV light-mediated hydrosilylation can be applied to the surface chemistry of silicon nanoparticles. The efficiencies of hydrosilylation for thermal-, radical- and Lewis acid-mediated reactions on silicon nanoparticles surfaces, deduced from the intensity of the ν(Si–H) absorption, are found to be comparable.     

Auxiliary basis sets for density-fitted correlated wavefunction calculations: weighted core-valence and ECP basis sets for post-d elements

We report optimised auxiliary basis sets for the resolution-of-the-identity (or density-fitting) approximation of two-electron integrals in second-order M?ller-Plesset perturbation theory (MP2) and similar electronic structure calculations with correlation-consistent basis sets for the post-d elements Ga-Kr, In-Xe, and Tl-Rn. The auxiliary basis sets are optimised such that the density-fitting error is negligible compared to the one-electron basis set error. To check to which extent this criterion is fulfilled we estimated for a test set of 80 molecules the basis set limit of the correlation energy at the MP2 level and evaluated the remaining density-fitting and the one-electron basis set errors. The resulting auxiliary basis sets are only 2-6 times larger than the corresponding one-electron basis sets and lead in MP2 calculations to speed-ups of the integral evaluation by one to three orders of magnitude. The density-fitting errors in the correlation energy are at least hundred times smaller than the one-electron basis set error, i.e. in the order of only 1-100 μH per atom.     

Discussing the U(1)-Problem of QED2without Instantons

We construct QED₂with mass and flavor and an extra Thirring term. The vacuum expectation values are carefully decomposed into clustering states using the U(1)-axial symmetry of the considered operators and a limiting procedure. The properties of the emerging expectation functional are compared to the proposedθ-vacuum of QCD. The massive theory is bosonized to a generalized Sine–Gordon model (GSG). The structure of the vacuum of QED₂manifests itself in symmetry properties of the GSG. We study the U(1)-problem and derive a Witten–Veneziano-type formula for the masses of the pseudoscalars determined from a semiclassical approximation.