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Updated: May 30, 2026

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Published on: May 30, 2014
Exact infinite-time statistics of the Loschmidt echo for a quantum quench
Lorenzo Campos Venuti1, N Tobias Jacobson, Siddhartha Santra
1Institute for Scientific Interchange, Torino, Italy.
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.
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