Hilbert space average of transition probabilities.,Physical Review E

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Hilbert space average of transition probabilities.
Physical Review E ( IF 2.2 ) Pub Date : 2020-06-22 , DOI: 10.1103/physreve.101.062135
Nico Hahn ₁ , Thomas Guhr ₁ , Daniel Waltner ₁

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The typicality approach and the Hilbert space averaging method as its technical manifestation are important concepts of quantum statistical mechanics. Extensively used for expectation values we extend them in this paper to transition probabilities. In this context we also find that the transition probability of two random uniformly distributed states is connected to the spectral statistics of the considered operator. Furthermore, within our approach we are capable to consider distributions of matrix elements between states that are not orthogonal. We will demonstrate our quite general result numerically for a kicked spin chain in the integrable resp. chaotic regime.

中文翻译：

希尔伯特空间转移概率的平均值。

典型性方法和希尔伯特空间平均法作为其技术表现形式是量子统计力学的重要概念。广泛用于期望值，我们在本文中将其扩展为转移概率。在这种情况下，我们还发现，两个随机均匀分布状态的跃迁概率与所考虑算子的频谱统计有关。此外，在我们的方法中，我们能够考虑非正交状态之间矩阵元素的分布。我们将在可积resp中以数值方式展示我们相当普遍的关于踢旋链的结果。混乱的政权。

更新日期：2020-06-22

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