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Register a new userAnalytic Bjorken flow in one-dimensional relativistic magnetohydrodynamics
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In the initial stage of relativistic heavy-ion collisions, strong magnetic fields appear due to the large velocity of the colliding charges. The evolution of these fields appears as a novel and intriguing feature in the fluid-dynamical description of heavy-ion collisions. In this work, we study analytically the one-dimensional, longitudinally boost-invariant motion of an ideal fluid in the presence of a transverse magnetic field. Interestingly, we find that, in the limit of ideal magnetohydrodynamics, i.e., for infinite conductivity, and irrespective of the strength of the initial magnetization, the decay of the fluid energy density $e$ with proper time $tau$ is the same as for the time-honored Bjorken flow without magnetic field. Furthermore, when the magnetic field is assumed to decay $sim tau^{-a}$, where $a$ is an arbitrary number, two classes of analytic solutions can be found depending on whether $a$ is larger or smaller than one. In summary, the analytic solutions presented here highlight that the Bjorken flow is far more general than formerly thought. These solutions can serve both to gain insight on the dynamics of heavy-ion collisions in the presence of strong magnetic fields and as testbeds for numerical codes.
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We have studied analytically the longitudinally boost-invariant motion of a relativistic dissipative fluid with spin. We have derived the analytic solutions of spin density and spin chemical potential as a function of proper time $tau$ in the presence of viscous tensor and the second order relaxation time corrections for spin. Interestingly, analogous to the ordinary particle number density and chemical potential, we find that the spin density and spin chemical potential decay as $simtau^{-1}$ and $simtau^{-1/3}$, respectively. It implies that the initial spin density may not survive at the freezeout hyper-surface. These solutions can serve both to gain insight on the dynamics of spin polarization in relativistic heavy-ion collisions and as testbeds for further numerical codes.
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We show that a Bjorken expanding strongly coupled $mathcal{N}=4$ Supersymmetric Yang-Mills plasma can violate the dominant and also the weak energy condition in its approach to hydrodynamics (even though the chosen initial data satisfy these constraints). This suggests that nontrivial quantum effects may be needed to describe the onset of hydrodynamic behavior in heavy-ion collisions. Also, we investigate whether there is an upper bound for the initial entropy of the plasma. We find numerical evidence for such a bound in our simulations and show that close to it the system evolves with approximately zero entropy production at early times, even though it is far from equilibrium.
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