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arXiv · 1104.3232

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

Lorenzo Campos Venuti·N. Tobias Jacobson·Siddhartha Santra·Paolo Zanardi
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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.

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Lorenzo Campos Venuti, N. Tobias Jacobson, Siddhartha Santra, Paolo Zanardi. 2011-04-16. Exact infinite-time statistics of the Loschmidt echo for a quantum quench. https://doi.org/10.1103/physrevlett.107.010403

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