Long-time behavior and dynamic scaling properties of displacement fluctuations in the sine-Gordon chain

The long-time behavior of the displacement fluctuations in the sine-Gordon chain is studied in terms of the exponents c and d, characterizing the asymptotic time dependence of the meansquare displacement [Xl(t)-Xl(0)]2tc and of the correlation function {(1N)×l[Xl(t)-Xl(0)]}2td. Invoking the dynamic scaling hypothesis, it is shown that d=2c=2b, and the bounds 12<~1b<~1 are derived for the Hamiltonian case. The relativistic ideal-kink-gas picture leads to 1b=1. For a chain evolving according to a Langevin equation with large damping 1b=12 is obtained. © 1980 The American Physical Society.