Scale-invariant string evolution with friction

We study the effects of friction on the scaling evolution of string networks in condensed matter and cosmological contexts. We derive a generalized ‘‘one-scale’’ model with the string correlation length L and velocity v as dynamical variables. In nonrelativistic systems, we obtain a well-known L∝${\mathit{t}}^{1/2}$ law, showing that loop production is important. For electroweak cosmic strings, we show transient damped epoch scaling with L∝${\mathit{t}}^{5/4}$ (or, in the matter era, L∝${\mathit{t}}^{3/2}$). A low initial density implies an earlier period with L∝${\mathit{t}}^{1/2}$. For GUT strings, the approach to linear scaling L∝t is faster than previously estimated. © 1996 The American Physical Society.