title: Exact infinite-time statistics of the Loschmidt echo for a quantum quench.
abstract: The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this Letter 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, quasicritical 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.
authors.affiliation: Institute for Scientific Interchange, Torino, Italy.
authors.forename: Lorenzo
authors.initials: L
authors.lastname: Campos Venuti
authors.forename: N Tobias
authors.initials: NT
authors.lastname: Jacobson
authors.forename: Siddhartha
authors.initials: S
authors.lastname: Santra
authors.forename: Paolo
authors.initials: P
authors.lastname: Zanardi