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多费米子系统的信息论特征：基于精确可解模型的探索

Information-Theoretic Features of Many Fermion Systems: An Exploration Based on Exactly Solvable Models.

作者信息

Plastino Angel Ricardo, Monteoliva Diana, Plastino Angelo

机构信息

CeBio-Departamento de Ciencias Básicas, Universidad Nacional del Noroeste de la Prov. de Buenos Aires, CONICET, Junin 1988, Argentina.

UNLP-Comisión de Investigaciones Científicas Provincia de Buenos Aires La Plata, La Plata 1900, Argentina.

出版信息

Entropy (Basel). 2021 Nov 10;23(11):1488. doi: 10.3390/e23111488.

DOI:10.3390/e23111488
PMID:34828186
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC8625102/
Abstract

Finite quantum many fermion systems are essential for our current understanding of Nature. They are at the core of molecular, atomic, and nuclear physics. In recent years, the application of information and complexity measures to the study of diverse types of many-fermion systems has opened a line of research that elucidates new aspects of the structure and behavior of this class of physical systems. In this work we explore the main features of information and information-based complexity indicators in exactly soluble many-fermion models of the Lipkin kind. Models of this kind have been extremely useful in shedding light on the intricacies of quantum many body physics. Models of the Lipkin kind play, for finite systems, a role similar to the one played by the celebrated Hubbard model of solid state physics. We consider two many fermion systems and show how their differences can be best appreciated by recourse to information theoretic tools. We appeal to information measures as tools to compare the structural details of different fermion systems. We will discover that few fermion systems are endowed by a much larger complexity-degree than many fermion ones. The same happens with the coupling-constants strengths. Complexity augments as they decrease, without reaching zero. Also, the behavior of the two lowest lying energy states are crucial in evaluating the system's complexity.

摘要

有限量子多费米子系统对于我们当前对自然的理解至关重要。它们是分子、原子和核物理的核心。近年来，将信息和复杂性度量应用于各种类型的多费米子系统的研究开辟了一条研究路线，阐明了这类物理系统结构和行为的新方面。在这项工作中，我们探索了利普金型完全可解多费米子模型中信息和基于信息的复杂性指标的主要特征。这类模型在揭示量子多体物理的复杂性方面极其有用。对于有限系统，利普金型模型所起的作用类似于固态物理中著名的哈伯德模型所起的作用。我们考虑两个多费米子系统，并展示如何借助信息论工具最好地理解它们的差异。我们将信息度量作为比较不同费米子系统结构细节的工具。我们会发现，少费米子系统的复杂度比多费米子系统大得多。耦合常数强度也是如此。随着它们减小，复杂度增加，但不会降至零。此外，两个最低能态的行为对于评估系统的复杂度至关重要。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/8085096ca96e/entropy-23-01488-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/f20b941fefeb/entropy-23-01488-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/6a44decb01ca/entropy-23-01488-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/38e9466c504b/entropy-23-01488-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/a23c3c2ec7ce/entropy-23-01488-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/1179b4e52fe6/entropy-23-01488-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/da4a4ee1433b/entropy-23-01488-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/e70e3809e422/entropy-23-01488-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/9a6283f80dbf/entropy-23-01488-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/4bd4f5c7e14c/entropy-23-01488-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/8085096ca96e/entropy-23-01488-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/f20b941fefeb/entropy-23-01488-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/6a44decb01ca/entropy-23-01488-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/38e9466c504b/entropy-23-01488-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/a23c3c2ec7ce/entropy-23-01488-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/1179b4e52fe6/entropy-23-01488-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/da4a4ee1433b/entropy-23-01488-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/e70e3809e422/entropy-23-01488-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/9a6283f80dbf/entropy-23-01488-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/4bd4f5c7e14c/entropy-23-01488-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6385/8625102/8085096ca96e/entropy-23-01488-g010.jpg

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