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.
Highlights
The study of finite many-fermion systems has been enriched in recent years with the incorporation of new mathematical tools inspired in information theory
Models of the Lipkin kind play for finite systems a role similar to that of the celebrated Hubbard model for solid state physics [15]
We have discussed the quantum statistics of two well known exactly soluble finite many fermion systems that the Literature shows to have been extremely useful in shedding light on the intricacies of quantum many fermion physics
Summary
The study of finite many-fermion systems has been enriched in recent years with the incorporation of new mathematical tools inspired in information theory. It is desirable to incorporate exactly soluble models to the ongoing research program of applying information-theoretical tools to finite many-fermion physics. The aim of the present contribution is to apply information techniques to investigate the properties of exactly soluble many-fermion models akin to the celebrated Lipkin one. We will apply in this effort to exactly solvable fermion models the relatively new notions of disequilibrium and statistical complexity. Lipkinlike models are arguably the simplest non trivial finite many-fermion systems They constitute an ideal testing ground for the application of information theoretical methods to many-fermion systems so as to gain insights that the study of other, more realistic models, can not yield.
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