Density of kinks just after a quench in an underdamped system
  A quench in an underdamped one dimensional $\phi^4$ model is studied by analytical methods. The density of kinks just after the transition is proportional to the square root of the rate of the quench for slow quenches. If the quench is shorter that the relaxation time, then the density scales like the third root of the rate. 
Jacek Dziarmaga