Computer simulation studies of the soliton model: 3. Non-continuum regimes and soliton interactions

We continue the study of the sine-Gordon soliton model, performing stochastic molecular dynamics computer simulations for a wide range of both temperatures and coupling constants. We find three general regimes of behaviour: the continuum limit or non-interacting regime; the pinned or transition-state-theory (TST) limit, where soliton-phonon interactions are important; and the general non-continuum regime, where soliton-soliton interactions of ‘multiple soliton effects’ are important. In the non-continuum regime, the correlation function changes as a function of temperature and coupling constant. We expect that this will lead to deviations from the continuum limit temperature scaling and soliton energy scaling observed in the dynamics of sine-Gordon systems.