ScholarWorks@경상국립대학교

초록

After introducing the algebraic and representative properties of the extended Weyl-Heisenberg algebra along with its special case containing the Wigner algebra, a new deformed boson algebra involving the reflection operator is proposed. Such an algebra differs from the other well-known deformed particle algebras in the literature so that its number operator spectrum constitutes a novel deformed number called nu$\nu$-number, which is changed for both even n and odd n in its energy levels. As physical applications of the quantum algebra developed here, the thermostatistical properties of a gas model of the nu$\nu$-deformed bosons and the blackbody radiation phenomena covering the nu$\nu$-deformed photon gas are studied in detail. Another application is carried out onto lattice oscillations via the Debye crystal model containing the nu$\nu$-deformed phonons. The effects of nu$\nu$-deformation onto the low-temperature behavior of the model specific heat of the nu$\nu$-deformed Debye solid are explored and are compared with the results of both the standard phonon gas and the ones with the non-extensive Tsallis statistics. Finally, possible implications of our results on other application areas of research such as strongly correlated quantum matter and star formation in cosmological systems are concisely discussed.

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