We discuss the non-equilibrium steady states of the XY quantum chain in the presence of magnetization or energy currents. The current full states are generated by the coupling of the chain with quantum reservoirs. Thanks to the free fermionic structure of the XY chain, the dynamics is exactly solved. In particular, in the special case of repeated interactions reservoirs the correlation matrix is explicitly calculated and we show that the steady state can be described by a generalized Gibbs state.

Université de Nancy