Exploring the applicability of dissipative fluid dynamics to small systems by comparison to the Boltzmann equation

Abstract

[Background] Experimental data from heavy-ion experiments at RHIC-BNL and LHC-CERN are quantitatively described using relativistic fluid dynamics. Even p+A and p+p collisions show signs of collective behavior describable in the same manner. Nevertheless, small system sizes and large gradients strain the limits of applicability of fluid-dynamical methods. [Purpose] The range of applicability of fluid dynamics for the description of the collective behavior, and in particular of the elliptic flow, of small systems needs to be explored. [Method] Results of relativistic fluid-dynamical simulations are compared with solutions of the Boltzmann equation in a longitudinally boost-invariant picture. As initial condition, several different transverse energy-density profiles for equilibrated matter are investigated. [Results] While there is overall a fair agreement of energy- and particle-density profiles, components of the shear-stress tensor are more sensitive to details of the implementation. The highest sensitivity is exhibited by quantities influenced by properties of the medium at freeze-out. [Conclusions] For some quantities, like the shear-stress tensor, agreement between fluid dynamics and transport theory extends into regions of Knudsen numbers and inverse Reynolds numbers where relativistic fluid dynamics is believed to fail.

arXiv comment18 pages, 49 figures

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• ${}^{16}{\mathrm{O}}^{16}\mathrm{O}$ at RHIC and the LHC comparing $\alpha$ clustering vs substructure
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