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arXiv · 1704.01457

Roles of energy eigenstates and eigenvalues in equilibration of isolated quantum systems

Shaoqi Zhu·Biao Wu
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Abstract

We show that eigen-energies and energy eigenstates play different roles in the equilibration process of an isolated quantum system. Their roles are revealed numerically by exchanging the eigen-energies between an integrable model and a non-integrable model. We ?find that the structure of eigenenergies of a non-integrable model characterized by non-degeneracy ensures that quantum revival occurs rarely whereas the energy eigenstates of a non-integrable model suppress the fluctuations for the equilibrated quantum state. Our study is aided with a quantum entropy that describes how randomly a wave function is distributed in quantum phase space. We also demonstrate with this quantum entropy the validity of Berry's conjecture for energy eigenstates. This implies that the energy eigenstates of a non-integrable model appear indeed "random".

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Shaoqi Zhu, Biao Wu. 2017-04-05. Roles of energy eigenstates and eigenvalues in equilibration of isolated quantum systems. https://doi.org/10.1103/physreve.96.042124

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