Two-Parameter Modifications of Anyonic Statistics

  • M. Ya. Hornetska Ivan Franko National University of Lviv, Chair of theoretical physics
  • A. A. Rovenchak Ivan Franko National University of Lviv, Chair of theoretical physics
Keywords: fractional statistics, anyons, к-deformation, Polychronakos statistics, Haldane–Wu statistics, Gentile statistics


Two-parameter models of fractional statistics aimed at finding an expression for the occupation numbers of free anyons have been considered. Virial coefficients are found for statistics of several types: к-deformed Polychronakos and Haldane–Wu statistics, Polychronakos and Haldane–Wu statistics modified with the q-exponential in the bosonic limit, and incomplete and nonadditive Gentile statistics for various level-filling maxima. A relation between the anyonic statistics and various statistics of fractional types is found and analyzed.


A. Khare, Fractional Statistics and Quantum Theory (World Scientific, Singapore, 2005).

A. Rovenchak, Zh. Fiz. Dosl. 172, 2001 (2013).

G.S. Jeon and J.K. Jain, Phys. Rev. B 81, 035319 (2010).

G.S. Canright and M.D. Johnson, J. Phys. A 27, 3579 (1994).

M.T. Batchelor, X.W. Guan, and N. Oelkers, Phys. Rev. Lett. 96, 210402 (2006).

D.-V. Anghel, Phys. Scr. T 151, 014079 (2012).

Z. Ebadi, B. Mirza, and H. Mohammadzadeh, J. Cosmol. Astropart. Phys. 2013, 057 (2013).

S.N. Bose, Z. Phys. 26, 178 (1924).

A. Einstein, Sitzungsber. Preuss. Konigl. Akad. Wiss. phys.-math. Klasse, 261 (1924).

A. Einstein, Sitzungsber. Preuss. Konigl. Akad. Wiss. phys.-math. Klasse, 3 (1925).

P.A.M. Dirac, Proc. R. Soc. London A 112, 661 (1926).

E. Fermi, Z. Phys. 36, 902 (1926).

G. Gentile, Nuovo Cimento 17, 493 (1940).

J.M. Leinaas and J. Myrheim, Nuovo Cimento 37B, 1 (1977).

F. Wilczek, Phys. Rev. Lett. 49, 957 (1987).

A.P. Polychronakos, Phys. Rev. Lett. 84, 1268 (2000).

F. Mancarella, A. Trombettoni, and G. Mussardo, Nucl. Phys. B 867 [FS], 950 (2013).

F.E. Camino, W. Zhou, and V.J. Goldman, Phys. Rev. B 72, 155313 (2005).

F.D.M. Haldane, Phys. Rev. Lett. 67, 937 (1991).

Y. Wu, Phys. Rev. Lett. 73, 922 (1994).

A.M. Gavrilik and Y.A.Mishchenko, Ukr. J. Phys. 58, 1171 (2013).

A.M. Gavrilik and Y.A.Mishchenko, Nucl. Phys. B 891, 466 (2015).

A. Rovenchak, Eur. Phys. J. B 87, 175 (2014).

A. Rovenchak, Phys. Rev. A 89, 052116 (2014).

P. F. Borges, H. Boschi-Filho, and C. Farina, Mod. Phys. Lett. A 14, 1217 (1999).

S. Mashkevich, J. Myrheim, and K. Olaussen, Phys. Lett. B 382, 124 (1996).

A. Kristoffersen, S. Mashkevich, J. Myrheim, and K. Olaussen, Int. J. Mod. Phys. A 13, 3723 (1998).

A.P. Polychronakos, Phys. Lett. B 365, 202 (1996).

Q.A. Wang, Entropy 5, 220 (2003).

Y. Kaupp, S. Liraki, D. Tayurskii, A. Useinov, A. El Kaabouchi, L. Nivanen, B. Minisini, F. Tsobnang, A. Le M’ehaut’e, and Q.A. Wang, J. Low Temp. Phys. 150, 660 (2008).

G. Kaniadakis, Physica A 296, 405 (2001).

G. Kaniadakis, Entropy 15, 3983 (2013).

R.T. Delves, G.S. Joyce, and I.J. Zucker, Proc. R. Soc. Lond. A 453, 1177 (1997).

A. Rovenchak, Fiz. Nizk. Temp. 39, 1141 (2013).

A.A. Rovenchak, Physics of Bose Systems (Ivan Franko National University of Lviv, Lviv, 2015) (in Ukrainian).

C. Tsallis, J. Stat. Phys. 52, 479 (1988).

V. Kac and P. Cheung, Quantum Calculus (Springer, New York, 2002).

Y. Yang, S. Xie, W. Feng, and X. Wu, Mod. Phys. Lett. A 13, 879 (1998).

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

Springer Handbook of Materials Measurement Methods, edited by H. Czichos, T. Saito, and L. Smith (Springer, Berlin, 2006).

How to Cite
Hornetska, M., & Rovenchak, A. (2019). Two-Parameter Modifications of Anyonic Statistics. Ukrainian Journal of Physics, 61(2), 168.
General problems of theoretical physics