Quantum critical systems with dissipative boundaries

We study the effects of dissipative boundaries in many-body systems at continuous quantum transitions, when parameters Hamiltonian driving unitary dynamics are close to their critical values. As paradigmatic models, we consider fermionic wires subject interactions boundaries, associated with pumping or loss particles. They induced by couplings a Markovian baths, so that evolution system density matrix can be described Lindblad master equation. arising from variations and dissipation parameters, starting t=0 ground state Hamiltonian. Two different dynamic regimes emerge: (i) an early-time regime for times t ~ L, where competition between coherent incoherent drivings develops finite-size scaling, obtained extending scaling framework describing closed system, allow boundary dissipation; (ii) large-time L^3 whose describes late leading t->infty stationary states.