Exact infinite-time statistics of the Loschmidt echo for a quantum quench |
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Authors: | Campos Venuti Lorenzo Jacobson N Tobias Santra Siddhartha Zanardi Paolo |
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Institution: | Institute for Scientific Interchange, Torino, Italy. |
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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 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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