Quasiclassical quantisation and radiative decay of sine-Gordon solitons pinned by a micro-inhomogeneity

Dynamics of a sine-Gordon kink and small-amplitude breather bound on an attractive localised inhomogeneity are studied. The rates of energy emission from the kink oscillating near the inhomogeneity and from a quiescent breather performing internal oscillations are calculated. In the semiclassical approximation, discrete quantised energy spectra for the solitons of both types are found, with regard to field-theory corrections to a kink's particle-like spectrum and to strong distortion of the breather's shape. The rates of radiative energy emission are interpreted as finite widths of the quantised quasiclassical energy levels. Oscillations of the breather as a whole near the inhomogeneity are also considered.