Abstract
The existence of stationary distributions in a multicomponent Boltzmann equation using a non-additive kinetic energy composition rule for binary collisions is discussed. It is found that detailed balance is not achieved when —in contrast to the case of a single rule— several different composition rules are considered. The long-time behaviour of a simple momentum space model is explored numerically: saturating, heating and cooling solutions are presented. These results may be used in modelling the kinetics of multicomponent systems, such as hadronic fireballs or quark-gluon plasma.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. Haug, C. Ell, Phys. Rev. B 46, 2126 (1992).
V. Spička, P. Lipavský, Phys. Rev. E 59, R1291 (1999).
V. Spička, P. Lipavský, K. Moravetz, Phys. Lett. A 240, 160 (1998).
V. Spička, Lipavský, Phys. Rev. Lett. 73, 3439 (1994).
J. Knoll, F. Riek, Yu.B. Ivanov, D.N. Voskresensky, J. Phys. Conf. Ser. 35, 357 (2006) arXiv: nucl-th/0512040v1.
T.S. Biró, G. Kaniadakis, Eur. Phys. J. B 50, 3 (2006).
G. Kaniadakis, Eur. Phys. J. A 40, 275 (2009).
E. Molnár, T.S. Biró, Eur. Phys. J. A 48, 172 (2012).
G. Kaniadakis, Physica A 296, 405 (2001).
J.A.S. Lima, R. Silva, A.R. Plastino, Phys. Rev. Lett. 86, 2938 (2001).
L.P. Kadanoff, G. Baym, Quantum Statistical Mechanics (Benjamin, New York, 1962).
C. Greiner, S. Leupold, Ann. Phys. 270, 328 (1998).
W. Cassing, S. Juchem, Nucl. Phys. A 665, 377 (2000).
Yu.B. Ivanov, J. Knoll, D.N. Voskresensky, Nucl. Phys. A 672, 313 (2000).
O. Buss et al., Phys. Rep. 512, 1 (2012).
J. Rafelski, T. Sherman, Lect. Notes Phys 633, 377 (2004) arXiv: physics/0204011v2.
T.S. Biró, P. Ván, J. Zimányi, Phys. Rev. C 75, 034910 (2007).
M. Strickland et al., Phys. Rev. D 87, 025010 (2013).
Andreas Ipp, in JPCS Proceedings of ``Heavy Ion Collisions in the LHC Era'' (2012) arXiv:1210.5150v1.
T.S. Biró, A. Jakovác, Phys. Rev. Lett. 94, 132302 (2005).
P. Arnold, Phys. Rev. D 62, 036003 (2000).
T.S. Biró, EPL 84, 56003 (2008).
T.S. Biró, G. Purcsel, K. Ürmössy, Eur. Phys. J. A 40, 325 (2009).
R. Wang et al., Eur. Phys. J. B 85, 314 (2012).
M.H. Ernst et al., J. Stat. Phys. 124, 549 (2006).
A.V. Bobylev et al., J. Stat. Phys. 110, 333 (2003).
A.V. Bobylev et al., J. Stat. Phys 111, 403 (2003).
W. Cassing, Eur. Phys. J. ST 168, 3 (2009).
S. McNamara, W.R. Young, Phys. Fluids A 4, 496 (1992).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Horváth, M., Biró, T.S. Multicomponent modified Boltzmann equation and thermalization. Eur. Phys. J. Plus 129, 165 (2014). https://doi.org/10.1140/epjp/i2014-14165-4
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2014-14165-4