Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems

Details Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems

2009-07-21

arxiv.org/abs/0907.3731v2

Phys. Rev. Lett. 105, 250401 (2010)

Physics

Condensed Matter

Quantum Gases

4 pages, 2 figures + 8 pages, 4 figures of supplementary material; changed title, published version

Scientific paper

10.1103/PhysRevLett.105.250401

We consider the question of thermalization for isolated quantum systems after a sudden parameter change, a so-called quantum quench. In part icular we investigate the pre-requisites for thermalization focusing on the statistical properties of the time-averaged density matrix and o f the expectation values of observables in the final eigenstates. We find that eigenstates, which are rare compared to the typical ones sampled by the micro-canonical distribution, are responsible for the absence of thermalization of some infinite integrable models and play an important role for some non-integrable systems of finite size, such as the Bose-Hubbard model. We stress the importance of finite size effects for the thermalization of isolated quantum systems and discuss two alternative scenarios for thermalization, as well as ways to prune down the correct one.

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