International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China.
Collaborative Innovation Center of Quantum Matter, Beijing 100871, China.
Phys Rev E. 2017 Oct;96(4-1):042124. doi: 10.1103/PhysRevE.96.042124. Epub 2017 Oct 12.
We show that eigenenergies and energy eigenstates play different roles in the equilibration process of an isolated quantum system. Their roles are revealed numerically by exchanging the eigenenergies between an integrable model and a nonintegrable model. We find that the structure of eigenenergies of a nonintegrable model characterized by nondegeneracy ensures that quantum revival occurs rarely whereas the energy eigenstates of a nonintegrable 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 nonintegrable model appear indeed random.
我们表明，本征能和能量本征态在孤立量子系统的平衡过程中扮演着不同的角色。通过在可积模型和非积模型之间交换本征能，我们从数值上揭示了它们的作用。我们发现，由非简并性表征的非积模型的本征能结构确保了量子复苏很少发生，而非积模型的能量本征态抑制了平衡量子态的涨落。我们的研究借助于量子熵来辅助，量子熵描述了波函数在量子相空间中随机分布的程度。我们还利用这个量子熵证明了 Berry 猜想对于能量本征态的有效性。这意味着非积模型的能量本征态确实是随机的。
