The investigation of classical particle in the presence of fractional calculus

Chung, Won Sang; Zare, Soroush; Hassanabadi, H.; Křı́ž, Jan; Maghsoodi, E.

doi:10.31349/revmexfis.66.840

Cited by 4 publications

(3 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where We notice in (22) that N D 0 would be complex for 1 + 2θ < 0. This non-physical behavior imposes a strong condition on the Wigner parameter θ > −1/2, which in turn means that the Dunkl formalism can only describe ideal Bose gases in these regimes.…”

Section: Ideal Bose Gas In the Dunkl Formalismmentioning

confidence: 99%

Ideal Bose gas and blackbody radiation in the Dunkl formalism

F.¹,

Hamil²,

Lütfüoğlu³

et al. 2023

J. Stat. Mech.

View full text Add to dashboard Cite

Recently, deformed quantum systems have received lots of attention in the literature. Dunkl formalism differs from others by containing the difference-differential and reflection operator. It is one of the most interesting deformations since it let us discuss the solutions according to the even and odd solutions. In this work, we studied the ideal Bose gas and the blackbody radiation via the Dunkl formalism. To this end, we made a liaison between the coordinate and momentum operators with the creation and annihilation operators, which allowed us to obtain the expressions of the partition function, the condensation temperature, and the ground state population of the Bose gas. We found that Dunkl-condensation temperature increases with increasing θ value. In the blackbody radiation phenomena, we found how the Dunkl formalism modifies total radiated energy. Then, we examined the thermal quantities of the system. We found that the Dunkl deformation causes an increase in entropy and specific heat functions as well as in the total radiation energy. However, we observed a decrease in the Dunk-corrected Helmholtz free energy in this scenario. Finally, we found that the equation of state is invariant even in the considered formalism.

show abstract

Section: Ideal Bose Gas In the Dunkl Formalismmentioning

confidence: 99%

Ideal Bose gas and blackbody radiation in the Dunkl formalism

F.¹,

Hamil²,

Lütfüoğlu³

et al. 2023

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

“…Dunkl-Newton mechanics, Dunkl-electrostatics and Dunkl-Maxwell equations are constructed in [50,51], respectively. Recent studies in Dunkl-general relativity and Dunkl-black hole thermodynamics are given in [52,53].…”

Section: Introductionmentioning

confidence: 99%

The Condensation of Ideal Bose Gas in a Gravitational Field in the Framework of Dunkl-Statistic

Hamil

Lütfüoğlu²

2023

Preprint

View full text Add to dashboard Cite

“…(a) E-mail: meradm@gmail.com (corresponding author) the Dunkl-Coulomb problem and its generalization in arbitrary dimensions in [14][15][16][17], the Dunkl derivative relative to time is also considered [18] and it has been adopted to study the ideal Bose gas and blackbody radiation [19] and the condensation of idea Bose in a gravitational field [20].…”

mentioning

confidence: 99%