  We study the quantum dynamics resulting from preparing a one-dimensional
quantum system in the ground state of initially two decoupled parts which are
then joined together (local quench). Specifically we focus on the transverse
Ising chain and compute the time-dependence of the magnetization profile,
m_l(t), and correlation functions at the critical point, in the
ferromagnetically ordered phase and in the paramagnetic phase. At the critical
point we find finite size scaling forms for the nonequilibrium magnetization
and compare predictions of conformal field theory with our numerical results.
In the ferromagnetic phase the magnetization profiles are well matched by our
predictions from a quasi-classical calculation.
