Semiclassical theory of finite temperature dynamics of the sine-Gordon model

We investigate the finite temperature dynamics of the sine-Gordon model by studying its dynamical correlation functions at low temperatures in the semiclassical approach. Going beyond previous analyses based on perfectly reflective or transmissive collision dynamics of the gapped solitonic excitations, we focus on the generic case when both transmissive and reflective scatterings are present. We argue that the universal behaviour of the correlation functions is qualitatively different from both special cases. In particular, the autocorrelation function decays in time neither exponentially nor as a power-law, but assumes a squeezed exponential form. Supporting our claim, we perform semiclassical Monte Carlo simulations utilizing the exact S-matrix of the model, and we construct an approximate analytic description based on the symmetric exclusion process.