Exact Mass-Coupling Relation for the Homogeneous Sine-Gordon Model.

We derive the exact mass-coupling relation of the simplest multiscale quantum integrable model, i.e., the homogeneous sine-Gordon model with two mass scales.

Continuous-time random-walk theory of interfering diffusion and chemical reaction with an application to electrochemical impedance spectra of oxidized Zr-1%Nb.

A microscopic theory is developed for the interplay of diffusion and chemical reaction and the results are compared with electrode impedance measurements on an oxide electrode. The theory is based on the ideas of continuous-time random walk and accounts for the interference of diffusion and recombination of the charge carriers in the oxide. The treatment results in a dispersive diffusivity with two time constants, one of them corresponding to the random walk, the other to the reaction.