New deformed boson algebra involving reflection operator and its implications to thermostatistics

Abstract

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu $$\end{document}-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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu $$\end{document}-deformed bosons and the blackbody radiation phenomena covering the nu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu $$\end{document}-deformed photon gas are studied in detail. Another application is carried out onto lattice oscillations via the Debye crystal model containing the nu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu $$\end{document}-deformed phonons. The effects of nu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu $$\end{document}-deformation onto the low-temperature behavior of the model specific heat of the nu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu $$\end{document}-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.