Quantum thermodynamics of the edge modes

By analyzing autocorrelation functions (ACF), we investigated different aspects, the relaxation and the information propagation, of a locally perturbed out-of-equilibrium quantum many-body system. Specifically, we studied time-ordered and out-of-time-ordered ACF, connecting these quantities to the average work (for a weak process) and the local contribution for the second moment of a work distribution in a wing-flap protocol, respectively. To exemplify our findings, we consider a spin-1/2 chain with an impurity at its edge, which has the role of producing localized edge modes. We derived analytical results that show that, in general, the presence of the localized edge states implies a slower relaxation and the phenomena of information trapping near the edge.