Why is it interesting to study "quantum quench" at a critical point? In the presentation, "Quantum Quenches in Extended Systems",  by S. Sotiriadis, P. Calabrese and J. Cardy, it was pointed out that quatum quench through a critical point remains an open problem. Why is it interesting to study quantum quenches along the critical point(s)? In doing so, what are the insights that you're going to get?
 A: The dynamics of a system quenched through a critical point are strongly affected by the critical physics. We can therefore learn about critical physics by looking at such systems. For example, it's possible to measure equilibrium critical exponents by varying the speed of the quench. Moreover, critical quench dynamics is very interesting because there is the possibility to observe universal non-equilibrium dynamics. For example, in the case of a sudden quench, original non-equilibrium critical exponents can be measured in the relaxation to equilibrium.
As a rule of thumb, anything 'critical' is interesting. This is because critical systems are strongly correlated and display emergent properties such as universality. You can't guess the collective behaviour by looking at single particles. Universality is not only fascinating, it is also really useful. Once you have identified your universality class, you can use a toy model for calculations and get accurate experimentally measurable predictions.
The most famous example is the Kibble-Zurek mechanism. There the system is dragged adiabatically (at first) to a critical point. As the critical point is approached, the correlation time of the system diverges and the quench stops being adiabatic. Then, the system does not thermalise completely and retains a finite correlation length. The slower you quench, the larger the correlation length. It turns out that there is a simple scaling relation between the correlation length and the quench speed which is universal and contains the equilibrium critical exponents. Take a look at the link for more details.
