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Quantum quenches in the sine--Gordon model: a semiclassical approach

We compute the time evolution of correlation functions after quantum quenches in the sine--Gordon model within the semiclassical approximation which is expected to yield accurate results for small quenches. We demonstrate this by reproducing results of a recent form factor calculation of the relaxation of expectation values. Extending these results, we find that the expectation values of most vertex operators do not decay to zero. We give analytic expressions for the relaxation of dynamic correlation functions, and we show that they have diffusive behavior for large timelike separation.