Ideal Bose Gas in Some Deformed Types of Thermodynamics. Correspondence between Deformation Parameters

  • O. M. Chubai Ivan Franko National University of Lviv, Department for Theoretical Physics
  • A. A. Rovenchak Ivan Franko National University of Lviv, Department for Theoretical Physics
Keywords: q- and м-deformed thermodynamics, q- and м-deformed algebras, Jackson derivative, cluster integrals, virial coefficients, non-additive Polychronakos statistics

Abstract

Two approaches to the construction of thermodynamics in the framework of the q- and м-formalisms, which correspond to certain deformations of the algebra of the creation–annihilation operators, have been considered. By comparing the obtained results, an approximate, independent of the space dimension, correspondence was revealed between the second virial coefficients for the ideal q- and м-deformed Bose gases. The corresponding discrepancy arises only at the level of the third virial coefficient. A method for emulating the м-deformed Bose gas up to the third virial coefficient inclusive by means of the two-parametric nonadditive Polychronakos statistics is demonstrated.

References

G. Gentile. Osservazioni sopra le statistiche intermedie. Nuovo Cimento 17, 493 (1940). https://doi.org/10.1007/BF02960187

G. Gentile. Le statistiche intermedie e le propriet'a dell'elio liquido. Nuovo Cimento 19, 109 (1942). https://doi.org/10.1007/BF02960192

H. Einbinder. Quantum statistics and the ℵ theorem. Phys. Rev. 74, 805 (1948). https://doi.org/10.1103/PhysRev.74.805

H.S. Green. A generalized method of field quantization. Phys. Rev. 90, 270 (1953). https://doi.org/10.1103/PhysRev.90.270

J. M. Leinaas, J. Myrheim. On the theory of identical particles. Nuovo Cimento B 37, 1 (1977). https://doi.org/10.1007/BF02727953

F.D.M. Haldane. "Fractional statistics" in arbitrary dimension: A generalization of the Pauli principle. Phys. Rev. Lett. 67, 937 (1991). https://doi.org/10.1103/PhysRevLett.67.937

Y.-S. Wu. Statistical distribution for generalized ideal gas of fractional-statistics particles. Phys. Rev. Lett. 73, 922 (1994). https://doi.org/10.1103/PhysRevLett.73.922

A.P. Polychronakos. Probabilities and path-integral realization of exclusion statistics. Phys. Lett. B 365, 202 (1996). https://doi.org/10.1016/0370-2693(95)01302-4

D.-V. Anghel. Fractional exclusion statistics: the method for describing interacting particle systems as ideal gases. Phys. Scr. T 151, 014079 (2012). https://doi.org/10.1088/0031-8949/2012/T151/014079

I.O. Vakarchuk, G. Panochko. The effective mass of an impurity atom in the Bose liquid with a deformed Heisenberg algebra. Ukr. J. Phys. 62, 123 (2017). https://doi.org/10.15407/ujpe62.02.0123

Z. Ebadi, B. Mirza, H. Mohammadzadeh. Infinite statistics condensate as a model of dark matter. J. Cosmol. Astropart. Phys. 11, 057 (2013). https://doi.org/10.1088/1475-7516/2013/11/057

A. Guha, P.S. Bhupal Dev, P.K. Das. Model-independent astrophysical constraints on leptophilic Dark Matter in the framework of Tsallis statistics. J. Cosmol. Astropart. Phys. 2019, 032 (2019). https://doi.org/10.1088/1475-7516/2019/02/032

M. Arik, D. D. Coon. Hilbert spaces of analytic functions and generalized coherent states. J. Math. Phys. 17, 524 (1976). https://doi.org/10.1063/1.522937

L.C. Biedenharn. The quantum group SUq(2) and a q-analogue of the boson operators. J. Phys. A 22, L873 (1989). https://doi.org/10.1088/0305-4470/22/18/004

A. Macfarlane. On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q. J. Phys. A 22, 4581 (1989). https://doi.org/10.1088/0305-4470/22/21/020

O.W. Greenberg. Example of infinite statistics. Phys. Rev. Lett. 64, 705 (1990). https://doi.org/10.1103/PhysRevLett.64.705

A. Jannussis. New deformed Heisenberg oscillator. J. Phys. A 26, L233 (1993). https://doi.org/10.1088/0305-4470/26/5/011

I.M. Burban. On (p, q; a, b, l)-deformed oscillator and its generalized quantum Heisenberg-Weyl algebra. Phys. Lett. A 366, 308 (2007). https://doi.org/10.1016/j.physleta.2007.02.051

A.M. Gavrilik, I.I. Kachurik. Nonstandard deformed oscillators from q- and p, q-deformations of Heisenberg algebra. SIGMA 12, 047 (2016). https://doi.org/10.3842/SIGMA.2016.047

W.S. Chung, A. Algin. Modified multi-dimensional q-deformed Newton oscillators: Algebra, interpolating statistics and thermodynamics. Ann. Phys. 409, 167911 (2019). https://doi.org/10.1016/j.aop.2019.167911

A. Algin, A. Olkun. Bose-Einstein condensation in low dimensional systems with deformed bosons. Ann. Phys. 383, 239 (2017). https://doi.org/10.1016/j.aop.2017.05.021

H. Mohammadzadeh, Y. Azizian-Kalandaragh, N. Cheraghpour, F. Adli. Thermodynamic geometry, condensation and Debye model of two-parameter deformed statistics. J. Stat. Mech.Theor. Exp. 2017, 083104 (2017). https://doi.org/10.1088/1742-5468/aa7ee0

A.M. Gavrilik, Yu.A. Mishchenko. Correlation function intercepts for ˜м, q-deformed Bose gas model implying effective accounting for interaction and compositeness of particles. Nucl. Phys. B 891, 466 (2015). https://doi.org/10.1016/j.nuclphysb.2014.12.017

A.M. Gavrilik, I.I. Kachurik, M.V. Khelashvili, A.V. Nazarenko. Condensate of м-Bose gas as a model of dark matter. Physica A 506, 835 (2018). https://doi.org/10.1016/j.physa.2018.05.001

M.Maleki, H.Mohammadzadeh, Z. Ebadi, M. Nattagh Najafi. Deformed boson condensate as a model of dark matter. Preprint arXiv:1912.04656.

J.A. Tuszy'nski, J.L. Rubin, J. Meyer, M. Kibler. Statistical mechanics of a q-deformed boson gas. Phys. Lett. A 175, 173 (1993). https://doi.org/10.1016/0375-9601(93)90822-H

A. Lavagno, P. Narayana Swamy. Thermostatistics of a q-deformed boson gas. Phys. Rev. E 61, 1218 (2000). https://doi.org/10.1103/PhysRevE.61.1218

A.M. Gavrilik, I.I. Kachurik, Yu.A. Mishchenko. Two-fermion composite quasi-bosons and deformed oscillators. Ukr. J. Phys. 56, 948 (2011).

A.P. Rebesh, I.I. Kachurik, A.M. Gavrilik. Elements of м-calculus and thermodynamics of м-bose gas model. Ukr. J. Phys. 58, 1182 (2013). https://doi.org/10.15407/ujpe58.12.1182

V. Kac, P. Cheung. Quantum Calculus (Springer, 2002). https://doi.org/10.1007/978-1-4613-0071-7

A. Lavagno, P. Narayana Swamy. Generalized thermodynamics of q-deformed bosons and fermions. Phys. Rev. E 65, 036101 (2002). https://doi.org/10.1103/PhysRevE.65.036101

A. Lavagno, A.M. Scarfone, P. Narayana Swamy. q-deformed structures and generalized thermodynamics. Rep. Math. Phys 55, 423 (2005). https://doi.org/10.1016/S0034-4877(05)80056-4

F.H. Jackson. On q-functions and a certain difference operator. Trans. Roy. Soc. Edin. 46, 253 (1909). https://doi.org/10.1017/S0080456800002751

A. Khare. Fractional Statistics and Quantum Theory (World Scientific, 2005). https://doi.org/10.1142/5752

A. Rovenchak. Two-parametric fractional statistics models for anions. Eur. Phys. J. B 87, 175 (2014). https://doi.org/10.1140/epjb/e2014-50171-8

A.A. Rovenchak. Exotic Statistics (Lviv University Press, 2018) (in Ukrainian). [ISBN: 978-617-10-0461-0].

L. Salasnich. BEC in nonextensive statistical mechanics. Int. J. Mod. Phys. B 14, 405 (2000). https://doi.org/10.1142/S0217979200000388

A.M. Gavrilik, A.P. Rebesh. Deformed gas of p, q-bosons: Virial expansion and virial coefficients. Mod. Phys. Lett. B 25, 1150030 (2012). https://doi.org/10.1142/S0217984911500308

A. Rovenchak. Weakly nonadditive Polychronakos statistics. Phys. Rev. A 89, 052116 (2014). https://doi.org/10.1103/PhysRevA.89.052116

C. Tsallis. What are the numbers that experiments provide? Qu'ımica Nova 17, 468 (1994).

T. Yamano. Some properties of q-logarithm and q-exponential functions in Tsallis statistics. Physica A 305, 486 (2002). https://doi.org/10.1016/S0378-4371(01)00567-2

A. Rovenchak. Ideal Bose-gas in nonadditive statistics. Low Temp. Phys. 44, 1025 (2018). https://doi.org/10.1063/1.5055843

Published
2020-06-09
How to Cite
Chubai, O., & Rovenchak, A. (2020). Ideal Bose Gas in Some Deformed Types of Thermodynamics. Correspondence between Deformation Parameters. Ukrainian Journal of Physics, 65(6), 500. https://doi.org/10.15407/ujpe65.6.500
Section
General physics