Paramagnetic squeezing of a uniformly expanding quark-gluon plasma in and out of equilibrium

• Published in: arXiv.org
• Main Authors: Sadooghi, N, Tabatabaee, S M A
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 01.10.2019
• Subjects: Anisotropy; Boltzmann transport equation; Computational fluid dynamics; Differential equations; Distribution functions; Energy dissipation; Fluid flow; Flux density; Gluons; Hydrodynamics; Ideal fluids; Ionic collisions; Magnetic fields; Magnetic permeability; Magnetization; Paramagnetism; Parameters; Physics - High Energy Physics - Lattice; Physics - High Energy Physics - Phenomenology; Physics - Nuclear Theory; Physics - Strongly Correlated Electrons; Quark-gluon plasma; Quarks; Temperature dependence; Time dependence; Viscous fluids
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1901.06928

The plasma of quarks and gluons created in ultrarelativistic heavy-ion collisions turns out to be paramagnetic. In the presence of a background magnetic field, this paramagnetism thus leads to a pressure anisotropy, similar to anisotropies appearing in a viscous fluid. In the present paper, we use this analogy, and develop a framework similar to anisotropic hydrodynamics, to take the pressure anisotropy caused, in particular, by the nonvanishing magnetization of a plasma of quarks and gluons into account. We consider the first two moments of the classical Boltzmann equation in the presence of an electromagnetic source in the relaxation-time approximation, and derive a set of coupled differential equations for the anisotropy parameter \(\xi_0\) and the effective temperature \(\lambda_0\) of an ideal fluid with nonvanishing magnetization. We also extend this method to a dissipative fluid with finite magnetization in the presence of a strong and dynamical magnetic field. We present a systematic method leading to the one-particle distribution function of this magnetized dissipative medium in a first-order derivative expansion, and arrive at analytical expressions for the shear and bulk viscosities in terms of the anisotropy parameter \(\xi\) and effective temperature \(\lambda\). We then solve the corresponding differential equations for \((\xi_0,\lambda_0)\) and \((\xi,\lambda)\) numerically, and determine, in this way, the proper time and temperature dependence of the energy density, directional pressures, speed of sound, and the magnetic susceptibility of a longitudinally expanding magnetized quark-gluon plasma in and out of equilibrium.