String Evolution with Friction

TL;DR

This paper investigates how friction influences the evolution of string networks in both condensed matter and cosmological settings, deriving a generalized model that captures different scaling behaviors over time.

Contribution

It introduces a generalized one-scale model for string evolution incorporating friction effects, revealing new scaling laws in various physical regimes.

Findings

In non-relativistic systems, string length scales as t^{1/2}.

Electroweak strings exhibit transient damped scaling with L∝ t^{5/4} or t^{3/2}.

GUT strings approach linear scaling faster than previously thought.

Abstract

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 non-relativistic systems, we obtain a well-known $L\propto t^{1/2}$ law, showing that loop production is important. For electroweak cosmic strings, we show transient damped epoch scaling with $L\propto t^{5/4}$ (or, in the matter era, $L\propto t^{3/2}$). A low initial density implies an earlier period with $L\propto t^{1/2}$. For GUT strings, the approach to linear scaling $L\propto t$ is faster than previously estimated.