Article
Version 1
Preserved in Portico This version is not peer-reviewed
Magic Numbers and Mixing Degree in Many-Fermion Systems
Version 1
: Received: 6 July 2023 / Approved: 7 July 2023 / Online: 7 July 2023 (10:51:53 CEST)
A peer-reviewed article of this Preprint also exists.
Monteoliva, D.; Plastino, A.; Plastino, A.R. Magic Numbers and Mixing Degree in Many-Fermion Systems. Entropy 2023, 25, 1206. Monteoliva, D.; Plastino, A.; Plastino, A.R. Magic Numbers and Mixing Degree in Many-Fermion Systems. Entropy 2023, 25, 1206.
Abstract
We consider an $N$ fermion system at low temperature $T$ in which we encounter special particle number values $N_m$ exhibiting special traits. These
values arise in focusing attention upon the degree of mixture (DM) of the pertinent quantum states. Given the coupling constant of the Hamiltonian, the DMs stay constant for all $N$-values, but experience sudden jumps at the $N_m$. For a quantum state described by the matrix $\rho$, its purity is expressed by $Tr \rho^2$ and then the degree of mixture is given by $1 - Tr \rho^2$, a quantity that coincides with the entropy $S_q$ for $q=2$. Thus, Tsallis entropy of index two faithfully represents the degree of mixing of a state, that is, it measures the extent to which the state departs from maximal purity . Macroscopic manifestations of the degree of mixing can be observed through various physical quantities. Our present study is closely related to properties of many-fermion systemsn that are usually manipulated at zero temperature. Here we wish to study the subject at finite temperature. Gibbs' ensemble is appealed to. Some interesting insights are thereby gained.
Keywords
Tsallis entropy; Many fermion systems; Mixture-degree; Finite temperature; Magic numbers
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment