preprints.org > physical sciences > mathematical physics > doi: 10.20944/preprints202307.0480.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 6 July 2023 / Approved: 7 July 2023 / Online: 7 July 2023 (10:51:53 CEST)

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.

Tsallis entropy; Many fermion systems; Mixture-degree; Finite temperature; Magic numbers

Physical Sciences, Mathematical Physics

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