  In this letter we show how the topological number of a static Hamiltonian can
be measured from a dynamical quench process. We focus on a two-band Chern
insulator in two-dimension, for instance, the Haldane model, whose dynamical
process can be described by a mapping from the $[k_x,k_y,t]$ space to the Bloch
sphere, characterized by the Hopf invariant. Such a mapping has been
constructed experimentally by measurements in cold atom systems. We show that,
taking any two constant vectors on the Bloch sphere, their inverse images of
this mapping are two trajectories in the $[k_x,k_y,t]$ space, and the linking
number of these two trajectories exactly equals to the Chern number of the
static Hamiltonian. Applying this result to a recent experiment from the
Hamburg group, we show that the linking number of the trajectories of the phase
vortices determines the phase boundary of the static Hamiltonian.

Quantum Gases;Strongly Correlated Electrons