Loschmidt echo of local dynamical processes in integrable and non integrable spin chains

Abstract

We consider a local instantaneous quantum dynamical process (QDP) that disturbs the background unitary Hamiltonian dynamics of a spin chain. We consider both a non-unitary incoherent QDP and a coherent unitary QDP intervention of the dynamical evolution of the spin chain. To track the effect of QDP on the dynamics, we investigate the Loschmidt echo, which is quite sensitive to whether the background dynamics is integrable or not. For the integrable case, namely the Heisenberg model, the Loschmidt echo depends on the parameters corresponding to the QDP as well as the time of occurrence of QDP. The probability of reviving the system to its initial state is higher for non-unitary/incoherent QDPs occurring at large time intervals. In the case of a unitary/coherent QDP, some amount of the probability of reviving the state is lost. For the non-integrable background dynamics we consider a kicked Harper model. It exhibits a decaying behaviour when contrasted with integrable dynamics. The decay rate is slower when the corresponding classical Hamiltonian is non-chaotic.