Bose-Einstein Condensation of q-Deformed Bosons Harmonically Trapped on Sierpiński Carpet and Menger Sponge

I.A. Sadiq, M.A.Z. Habeeb Department of Physics, College of Science, Al-Nahrain University, Jaderyia, Baghdad, Iraq

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Bose-Einstein condensation, as a fifth state of matter, can only occur under certain conditions. One of those conditions is the spatial dimensions confining the bosonic systems. We investigated Bose-Einstein condensation for a finite number of harmonically trapped bosons on fractal structures. The investigation involves two approaches; one belongs to standard Bose-Einstein statistics, and the other belongs to the theory of q-deformed bosons. The properties of Bose-Einstein condensates in the two approaches are computed by performing the sum over the energy states. From these two approaches, we attempt to gain insight into the possibility of using q-numbers to assign fractal dimensions via Bose-Einstein condensation. In this endeavor, the bosons are considered ideal to emphasize that the parameter q only represents the fractal dimension of the structures confining the bosons. The results reveal that a condensate of q-deformed bosons with q=0.74 is adequate to represent a condensate of standard bosons on a Sierpiński carpet. The results also reveal that a condensate of q-deformed bosons with q=0.33 is adequate to represent a condensate of standard bosons on a Menger sponge. We also suggest an expression for using the parameter q to measure the interaction between bosons harmonically trapped on fractal structures, which may also help to study the effect of porosity or fractal dimension on the interaction between bosons.

DOI:10.12693/APhysPolA.144.234 topics: Bose-Einstein condensation, q-deformed bosons, Tsallis nonextensive parameter, fractal dimensions