AUTHOR=Gavrilik A. M. , Kachurik I. I. , Nazarenko A. V. 

TITLE=New deformed Heisenberg algebra from the μ-deformed model of dark matter

JOURNAL=Frontiers in Astronomy and Space Sciences

VOLUME=10

YEAR=2023

URL=https://www.frontiersin.org/journals/astronomy-and-space-sciences/articles/10.3389/fspas.2023.1133976

DOI=10.3389/fspas.2023.1133976

ISSN=2296-987X

ABSTRACT=<p>Recently, the <italic>μ</italic>-deformation-based approach to modeling dark matter, which exploits <italic>μ</italic>-deformed thermodynamics, was extended to the study of galaxy halo density profile and of the rotation curves of a number of (dwarf or low brightness) galaxies. For that goal, <italic>μ</italic>-deformed analogs of the Lane–Emden equation (LEE) have been proposed, and their solutions describing density profiles obtained. There are two seemingly different versions of <italic>μ</italic>-deformed LEE which possess the same solution, and so we deal with their equivalence. From the latter property we derive new, rather unusual, <italic>μ</italic>-deformed Heisenberg algebra (HA) for the position and momentum operators, and present the <italic>μ</italic>-HA in few possible forms (each one at <italic>μ</italic> → 0 recovers usual HA). The generalized uncertainty relation linked with the new <italic>μ</italic>-HA is studied, along with its interesting implications including the appearance of the quadruple of both maximal and minimal lengths and momenta.</p>