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

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

2011-04-16

arxiv.org/abs/1104.3232v1

Phys. Rev. Lett. 107, 010403 (2011)

Physics

Quantum Physics

4 pages, 2 figures

Scientific paper

10.1103/PhysRevLett.107.010403

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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