Applications of Supersymmetric Polynomials in Statistical Quantum Physics

We propose a correspondence between the partition functions of ideal gases consisting of both bosons and fermions and the algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sided sequences ℓ1(Z0). Such an approach allows us to interpret some of the combinato...

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Veröffentlicht in:Quantum Reports 2023-12, Vol.5 (4), p.683-697
Hauptverfasser: Chernega, Iryna, Martsinkiv, Mariia, Vasylyshyn, Taras, Zagorodnyuk, Andriy
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Sprache:eng
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Zusammenfassung:We propose a correspondence between the partition functions of ideal gases consisting of both bosons and fermions and the algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sided sequences ℓ1(Z0). Such an approach allows us to interpret some of the combinatorial identities for supersymmetric polynomials from a physical point of view. We consider a relation of equivalence for ℓ1(Z0), induced by the supersymmetric polynomials, and the semi-ring algebraic structures on the quotient set with respect to this relation. The quotient set is a natural model for the set of energy levels of a quantum system. We introduce two different topological semi-ring structures into this set and discuss their possible physical interpretations.
ISSN:2624-960X
2624-960X
DOI:10.3390/quantum5040043