Loschmidt echo in many-spin systems: equilibration, localization and the emergent mechanisms of irreversibility (P. Zangara)

  Such an apparently irreversible process is known as spin diffusion and it can lead the system back to “equilibrium”. One can generalize this idea by considering a closed many-body quantum system which is departed from equilibrium and, as it evolves unitarily, many local observables have some transient behavior and then remain close to a static value. However, such an idea of equilibration in closed quantum systems soon faces limitations.On the one hand, the equilibration of the polarization is not always the rule as there are physical situations where the initial excitation cannot spread at all. This is the case of localization phenomena, which has recently generated intense debate as its onset constitutes an important ergodic to non-ergodic transition.

On the other hand, even in the cases where the system seems to have equilibrated, the unitarity of the quantum dynamics ensures a precise memory of the non-equilibrium initial condition. Then, if some experimental protocol could reverse the many-body dynamics, it would drive the system back to the initial non-equilibrium state. Such a general idea defines the Loschmidt echo (LE), which embodies the various time-reversal procedures implemented in nuclear magnetic resonance.

In this talk I will introduce the LE as a spin autocorrelation function and I will discuss its role as a dynamical witness in the context of equilibration and localization.   Additionally, I will show some numerical evidence on the emergent mechanisms that transform a -unitary driven- equilibration into an irreversible process in the thermodynamic limit.