Chernega, I.; Martsinkiv, M.; Vasylyshyn, T.; Zagorodnyuk, A. Applications of Supersymmetric Polynomials in Statistical Quantum Physics. Quantum Rep.2023, 5, 683-697.
Chernega, I.; Martsinkiv, M.; Vasylyshyn, T.; Zagorodnyuk, A. Applications of Supersymmetric Polynomials in Statistical Quantum Physics. Quantum Rep. 2023, 5, 683-697.
Chernega, I.; Martsinkiv, M.; Vasylyshyn, T.; Zagorodnyuk, A. Applications of Supersymmetric Polynomials in Statistical Quantum Physics. Quantum Rep.2023, 5, 683-697.
Chernega, I.; Martsinkiv, M.; Vasylyshyn, T.; Zagorodnyuk, A. Applications of Supersymmetric Polynomials in Statistical Quantum Physics. Quantum Rep. 2023, 5, 683-697.
Abstract
We propose a correspondence between partition functions of ideal gases consisting of both bosons and fermions and algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sides sequences ℓ1(Z0). Such an approach allows us to interpret some combinatorial identities for supersymmetric polynomials from a physical point of view. We consider a relation of equivalence on ℓ1(Z0) induced by the supersymmetric polynomials, and semiring 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 semiring structures on this set and discuss their possible physical interpretations.
Keywords
quantum ideal gas; grand partition function; supersymmetric polynomials on Banach spaces; algebraic basis; topological semiring; tropical semiring
Subject
Physical Sciences, Quantum Science and Technology
Copyright:
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