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 an Hamiltonian parameter at a certain velocity. General scaling laws are derived for the density of excitations and energy produced during the quench as a function of quench velocity and 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 equation of the problem is presented. 
Dario Patan\`e, Alessandro Silva, Luigi Amico, Rosario Fazio, Giuseppe   E. Santoro