Deformed Bose Gas Models Aimed at Taking into Account Both Compositeness of Particles and Their Interaction

  • A. M. Gavrilik Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
  • Yu. A. Mishchenko Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
Keywords: deformed oscillators, deformed Bose gas model, non-ideal Bose gas, virial expansion, modified Jackson derivative, virial coefficients, composite bosons

Abstract

We consider the deformed Bose gas model with the deformation structure function that is the combination of a q-deformation and a quadratically polynomial deformation. Such a choice of the unifying deformation structure function enables us to describe the interacting gas of composite (two-fermionic or two-bosonic) bosons. Using the relevant generalization of the Jackson derivative, we derive a two-parametric expression for the total number of particles, from which the deformed virial expansion of the equation of state is obtained. The latter is interpreted as the virial expansion for the effective description of a gas of interacting composite bosons with some interaction potential.

References

L.D. Landau and E.M. Lifshitz, Statistical Physics (Pergamon, New York, 1980).

K. Huang, Statistical Mechanics (Wiley, New York, 1987).

R.K. Pathria and P.D. Beale, Statistical Mechanics (Elsevier, Amsterdam, 2011).

M.D. Girardeau, J. Math. Phys. 16, 1901 (1975).

https://doi.org/10.1063/1.522742

D. Hadjimichef, G. Krein, S. Szpigel, and J.D. Veiga, Ann. Phys. 268, 105 (1998).

https://doi.org/10.1006/aphy.1998.5825

M. Combescot, O. Betbeder-Matibet, and F. Dubin, Phys. Rep. 463, 215 (2008).

https://doi.org/10.1016/j.physrep.2007.11.003

S. Meljanac, M. Milekovic, and S. Pallua, Phys. Lett. B 328, 55 (1994).

https://doi.org/10.1016/0370-2693(94)90427-8

V.I. Man'ko, G. Marmo, E.C.G. Sudarshan, and F. Zaccaria, Phys. Scripta 55, 528 (1997).

https://doi.org/10.1088/0031-8949/55/5/004

D. Bonatsos and C. Daskaloyannis, Prog. Part. Nucl. Phys. 43, 537 (1999).

https://doi.org/10.1016/S0146-6410(99)00100-3

C. Daskaloyannis, J. Phys. A: Math. Gen. 24, L789 (1991).

https://doi.org/10.1088/0305-4470/24/15/001

A. Lavagno and P. Narayana Swamy, Phys. Rev. E 61, 1218 (2000).

https://doi.org/10.1103/PhysRevE.61.1218

A. Lavagno and P. Narayana Swamy, Phys. Rev. E 65, 036101 (2002).

https://doi.org/10.1103/PhysRevE.65.036101

A.M. Gavrilik and A.P. Rebesh, Mod. Phys. Lett. B 25, 1150030 (2012).

https://doi.org/10.1142/S0217984911500308

A.M. Gavrilik, I.I. Kachurik, and Yu.A. Mishchenko, J. Phys. A: Math. Theor. 44, 475303 (2011).

https://doi.org/10.1088/1751-8113/44/47/475303

S.S. Avancini and G. Krein, J. Phys. A: Math. Gen. 28, 685 (1995).

https://doi.org/10.1088/0305-4470/28/3/021

M. Bagheri Harouni, R. Roknizadeh, and M.H. Naderi, J. Phys. B: At. Mol. Opt. Phys. 42, 095501 (2009).

https://doi.org/10.1088/0953-4075/42/9/095501

Y.-X. Liu, C.P. Sun, S.X. Yu, and D.L. Zhou, Phys. Rev. A 63, 023802 (2001).

https://doi.org/10.1103/PhysRevA.63.023802

Q. J. Zeng, Z. Cheng, and J.-H. Yuan, Eur. Phys. J. B 81, 275 (2011).

https://doi.org/10.1140/epjb/e2011-20004-7

O.W. Greenberg and R.C. Hilborn, Phys. Rev. Lett. 83, 4460 (1999).

https://doi.org/10.1103/PhysRevLett.83.4460

K.D. Sviratcheva et al., Phys. Rev. Lett. 93, 152501 (2004).

https://doi.org/10.1103/PhysRevLett.93.152501

D. Bonatsos and C. Daskaloyannis, Phys. Rev. A 46, 75 (1992).

https://doi.org/10.1103/PhysRevA.46.75

A.M. Gavrilik, I.I. Kachurik, and Yu.A. Mishchenko, Ukr. J. Phys. 56, 948 (2011).

A.M. Scarfone, and P. Narayana Swamy, J. Stat. Mech. 2009, 02055 (2009).

https://doi.org/10.1088/1742-5468/2009/02/P02055

A. Algin and M. Senay, Phys. Rev. E 85, 041123 (2012).

https://doi.org/10.1103/PhysRevE.85.041123

A.M. Gavrilik and Yu.A. Mishchenko, Phys. Lett. A 376, 1596 (2012).

https://doi.org/10.1016/j.physleta.2012.03.053

A.M. Gavrilik and Yu.A. Mishchenko, J. Phys. A: Math. Theor. 46, 145301 (2013).

https://doi.org/10.1088/1751-8113/46/14/145301

R. Parthasarathy and K. Viswanathan, preprint IMSc- 92/02-57 (1992).

D.V. Anchishkin, A.M. Gavrilik, and S.Y. Panitkin, Ukr. J. Phys. 49, 935 (2004).

A.M. Gavrilik, SIGMA 2, 074 (2006).

A.M. Gavrilik and A.P. Rebesh, Eur. Phys. J. A 47, 55 (2011).

https://doi.org/10.1140/epja/i2011-11055-x

Published
2018-10-11
How to Cite
Gavrilik, A., & Mishchenko, Y. (2018). Deformed Bose Gas Models Aimed at Taking into Account Both Compositeness of Particles and Their Interaction. Ukrainian Journal of Physics, 58(12), 1171. https://doi.org/10.15407/ujpe58.12.1171
Section
General problems of theoretical physics