  We study quench dynamics and defect production in the Kitaev and the extended
Kitaev models. For the Kitaev model in one dimension, we show that in the limit
of slow quench rate, the defect density n \sim 1/\sqrt{\tau} where 1/\tau is
the quench rate. We also compute the defect correlation function by providing
an exact calculation of all independent non-zero spin correlation functions of
the model. In two dimensions, where the quench dynamics takes the system across
a critical line, we elaborate on the results of earlier work [K. Sengupta, D.
Sen and S. Mondal, Phys. Rev. Lett. 100, 077204 (2008)] to discuss the
unconventional scaling of the defect density with the quench rate. In this
context, we outline a general proof that for a d dimensional quantum model,
where the quench takes the system through a d-m dimensional gapless (critical)
surface characterized by correlation length exponent \nu and dynamical critical
exponent z, the defect density n \sim 1/\tau^{m \nu /(z \nu +1)}. We also
discuss the variation of the shape and the spatial extent of the defect
correlation function with the change of both the rate of quench and the model
parameters and compute the entropy generated during such a quench process.
Finally, we study the defect scaling law, entropy generation and defect
correlation function of the two-dimensional extended Kitaev model.
