The concept of induced surface and curvature tensions for EoS of hard discs and hard spheres
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part of Springer Nature, 2020 https://doi.org/10.1140/epjst/e2020-000036-3
THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Regular Article
The concept of induced surface and curvature tensions for EoS of hard discs and hard spheres Nazar S. Yakovenko1 , Kyrill A. Bugaev1,2,a , Larissa V. Bravina3 , and Eugene E. Zabrodin3,4 1
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Department of Physics, Taras Shevchenko National University of Kyiv, 03022 Kyiv, Ukraine Bogolyubov Institute for Theoretical Physics, Metrologichna str. 14B , Kyiv 03680, Ukraine Department of Physics, University of Oslo, PB 1048 Blindern, 0316 Oslo, Norway Skobeltzyn Institute of Nuclear Physics, Moscow State University, 119899 Moscow, Russia Received 11 March 2020 / Accepted 27 October 2020 Published online 21 December 2020 Abstract. Mathematically rigorous derivation of the hadron matter equation of state (EoS) within the induced surface and curvature tensions approach is worked out. Such an EoS allows one to go beyond the Van der Waals approximation for the interaction potential of hard spheres. The compressibility of a single- and two-component hadron mixtures are found for two- and three-dimensional cases. The obtained results are compared to the well known one- and two-component EoS of hard spheres and hard discs. The values of the model parameters which successfully reproduce the well-known EoS on different intervals of packing fractions are determined from fitting their compressibility factors. It is argued that after some modification the developed approach can be also used to describe the mixtures of gases of convex hard particles of different sizes and shapes.
1 Introduction Elucidation of the effects of dense medium influence on the properties of interaction and, more generally, on the properties of constituents of the considered system is important, but the hard task of many-body theory. In particular, a gradual transition from the excluded volume regime which “works” at low densities in a gas of hard spheres to the eigen volume regime which should be used at high densities of hard spheres near the transition to a solid phase is well studied. But the question is how one can generate such a transition in case of several different hard-core radii for the relativistic systems in which the number of particles is not conserved. From the famous Isihara-Hadwiger (IH) formula [1–3] for the excluded volume of convex hard particles 2V excl = 2V eigen + S eigen (R1 + R2 ) one can easily deduce that at high densities either the surface term proportional to eigen surface S eigen of particle, or a
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The European Physical Journal Special Topics
the mean curvature radii R1 & R2 of particles should disappear from the IH equation, if one is able to account for the influence of the dense medium. More specifically, one can state that even in the simplest systems like the mixture of gases consisting of several kinds of particles with different hard-core radii, i.e. in a multicomponent case, there is a problem of how a dense thermal medium mod
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