量子多体系统的有序无序指数对复杂性分类（PODI）
Complexity classification of quantum many-body systems according to the Pair of Order-Disorder Indices (PODI)
摘要：
由Lopez-Ruiz，Mancini，and Calbet（LMC）和Shiner，Davison and Landsberg（SDL）定义的复杂性的统计测度被计算为四个量子多体系统（即原子、原子核、原子团簇和阱中的关联原子（玻色子））的粒子数的函数。对每个系统评估的一对有序和无序强度可以作为一对有序-无序指数（PODI），定量表征任何量子系统中的有序与无序。根据上述分类，我们认为玻色子具有无序的复杂性特征，原子具有有序的特征，而原子核和原子团簇的无序程度较低，介于两者之间。这个标准可以用来估计有序和无序对其他更复杂的量子系统的复杂性的相对贡献，甚至经典系统，如果人们能够概率地描述它们的话。我们还解决了这个问题，这些系统的复杂性是否会随着粒子数量的增加而增加。我们的比较研究表明，原子是四个量子系统中唯一有序的，具有自组织能力的量子系统。我们推测，这是一个信息论的原因，原子是适合作为生物学感兴趣的较大结构，即分子和大分子的积木。这是惠勒的“it from bit”的精神，这个项目是用信息论的方式来呈现宇宙的一切。
英文摘要：
The statistical measures of complexity defined by Lopez-Ruiz, Mancini, and Calbet (LMC) and Shiner, Davison and Landsberg (SDL) are calculated as functions of the number of particles for four quantum many-body systems, i.e. atoms, nuclei, atomic clusters, and correlated atoms in a trap (bosons). A pair of order and disorder strengths, evaluated for each system, can serve as a Pair of Order-Disorder Indices (PODI), characterizing quantitatively order versus disorder in any quantum system. According to the above classification, we assign to bosons the complexity character of disorder, to atoms the character of order, while nuclei and atomic clusters are (less) disordered and lie between them. This criterion can be used to estimate the relative contribution of order and disorder to complexity for other more complicated quantum systems as well and even classical ones, if one is able to describe them probabilistically. We also address the issue, whether those systems can grow in complexity as the number of particles increases. Our comparative study indicates that atoms are the only quantum system out of four, which is ordered, with the ability to self-organize. We conjecture that this is an information-theoretic reason that atoms are suitable as building blocks of larger structures of biological interest i.e. molecules and macromolecules. This is in the spirit of Wheeler's "it from bit" quote, the project to present everything about the Universe in terms of information theory.
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