Unitary Equilibrations: Temporal and Hilbert Space Typicality Loschmidt Echo

          @misc{ scivideos_PIRSA:10050064,
            doi = {10.48660/10050064},
            url = {https://pirsa.org/10050064},
            author = {Zanardi, Paolo},
            keywords = {Quantum Information},
            language = {en},
            title = {Unitary Equilibrations: Temporal and Hilbert Space Typicality Loschmidt Echo},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2010},
            month = {may},
            note = {PIRSA:10050064 see, \url{https://scivideos.org/pirsa/10050064}}
          }
          

Abstract

Closed quantum systems evolve unitarily and therefore cannot converge in a strong sense to an equilibrium state starting out from a generic pure state. Nevertheless for large system size one observes temporal typicality. Namely, for the overwhelming majority of the time instants, the statistics of observables is practically indistinguishable from an effective equilibrium one. In this talk we will discuss he Loschmidt echo (LE) to study this sort of unitary equilibration after a quench. In particular we ll address the issue of typicality with respect the initial state preparation and the influence of quantum criticality of the long-time probability distribution of LE.