论文标题
安德森本地化的观察性熵研究
Observational entropic study of Anderson localization
论文作者
论文摘要
在量子力学的背景下，热力学熵的概念是一个有争议的话题。尽管有提议将冯·诺伊曼熵视为热力学熵，但它具有自身的局限性。观察性熵是作为Boltzmann熵的概括而开发的，目前，它是对量子力学中热力学熵提供清晰且定义明确的理解的最有希望的候选者之一。在这项工作中，我们研究了一维Aubrey-André（AA）模型的定位 - 移位转变的观察性熵的行为。我们发现，对于典型的中谱状态，在离域阶段，观察熵的生长迅速增长，粗粒大小和饱和到最大值，而在局部阶段，生长是对数。此外，对于给定的粗粒，它随着到达阶段的系统大小而对数增加，并在局部阶段遵守面积定律。我们还发现观测熵的增加，然后是量子淬灭，在离域相以及过渡点的时间上是对数的，而在局部相中，IT振荡。最后，我们还使用动量空间粗粒剂冒险使用AA模型的自动划分特性。
The notion of the thermodynamic entropy in the context of quantum mechanics is a controversial topic. While there were proposals to refer von Neumann entropy as the thermodynamic entropy, it has it's own limitations. The observational entropy has been developed as a generalization of Boltzmann entropy, and it is presently one of the most promising candidates to provide a clear and well-defined understanding of the thermodynamic entropy in quantum mechanics. In this work, we study the behaviour of the observational entropy in the context of localization-delocalization transition for one-dimensional Aubrey-André (AA) model. We find that for the typical mid-spectrum states, in the delocalized phase the observation entropy grows rapidly with coarse-grain size and saturates to the maximal value, while in the localized phase the growth is logarithmic. Moreover, for a given coarse-graining, it increases logarithmically with system size in the delocalized phase, and obeys area law in the localized phase. We also find the increase of the observational entropy followed by the quantum quench, is logarithmic in time in the delocalized phase as well as at the transition point, while in the localized phase it oscillates. Finally, we also venture the self-dual property of the AA model using momentum space coarse-graining.
