Density of kinks just after a quench in an overdamped system

Abstract

A quench in an overdamped one dimensional ${\varphi }^4$ model is studied by analytical and numerical methods. For an infinite system or a finite system with free boundary conditions, the density of kinks after the transition is proportional to the eighth root of the rate of the quench. For a system with periodic boundary conditions, it is proportional to the fourth root of the rate. The critical exponent predicted in Zurek scenario is put in question.

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