Exact infinite-time statistics of the Loschmidt echo for a quantum quench

          @misc{ pirsa_PIRSA:11050026,
            doi = {10.48660/11050026},
            url = {https://pirsa.org/11050026},
            author = {Zanardi, Paolo},
            keywords = {Condensed Matter},
            language = {en},
            title = {Exact infinite-time statistics of the Loschmidt echo for a quantum quench},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {may},
            note = {PIRSA:11050026 see, \url{https://pirsa.org}}
          }
          

Abstract

The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this paper we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an exact expression for its long-time distribution for a closed system described by a quantum XY chain following a sudden quench. In the thermodynamic limit the logarithm of the Loschmidt echo becomes normally distributed, whereas for small quenches in the opposite, quasi-critical regime, the distribution function acquires a universal double-peaked form indicating poor equilibration. These findings, obtained by a central limit theorem-type result, extend to completely general models in the small-quench regime.