Adiabatic dynamics of a quantum critical system coupled to an environment: Scaling and kinetic equation approaches

We study the dynamics of open quantum many-body systems driven across a critical point by quenching a parameter of the Hamiltonian at a certain velocity. General scaling laws are derived for the density of excitations and of energy produced during the quench as a function of the quench velocity and the bath temperature. The scaling laws and their regimes of validity are verified for the XY spin chain locally coupled to bosonic baths. A detailed derivation and analysis of the kinetic equations for the problem is presented.