  A phase transition indicates a sudden change in the properties of a large
system. For temperature-driven phase transitions this is related to
non-analytic behavior of the free energy density at the critical temperature:
The knowledge of the free energy density in one phase is insufficient to
predict the properties of the other phase. In this paper we show that a close
analogue of this behavior can occur in the real time evolution of quantum
systems, namely non-analytic behavior at a critical time. We denote such
behavior a dynamical phase transition and explore its properties in the
transverse field Ising model. Specifically, we show that the equilibrium
quantum phase transition and the dynamical phase transition in this model are
intimately related.
