Thermal sine-Gordon system in the presence of different types of dissipation

The effects of thermal fluctuations on solitons and phonons of the sine-Gordon system are investigated in the presence of a α${\phi }_t$-β${\phi }_{\mathrm{xxt}}$ dissipation. The analysis requires the assumption of a more general autocorrelation function for the noise than the one used in previous works. We verify that this leads to the correct results for the average kinetic energies of solitons and phonons in the system. We also evaluate the linewidth for a Josephson oscillator in the presence of both α and β dissipation, and lastly we briefly discuss the extension of the theory to more general dissipative terms.