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Register a new userRelativistic fluctuating hydrodynamics with memory functions and colored noises
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Relativistic dissipative hydrodynamics including hydrodynamic fluctuations is formulated by putting an emphasis on non-linearity and causality. As a consequence of causality, dissipative currents become dynamical variables and noises appeared in an integral form of constitutive equations should be colored ones from fluctuation-dissipation relations. Nevertheless noises turn out to be white ones in its differential form when noises are assumed to be Gaussian. The obtained ifferential equations are very useful in numerical implementation of relativistic fluctuating hydrodynamics.
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We argue that different formulations of hydrodynamics are related to uncertainties in the definitions of local thermodynamic and hydrodynamic variables. We show that this ambiguity can be resolved by viewing different formulations of hydrodynamics as particular gauge choices which lead to the same physical behavior of the system. Using the example of bulk viscosity, we show that Bemfica-Disconzi-Noronha-Kovtun (BDNK) and Israel-Stewart hydrodynamics are particular gauge choices of this type, related by a well-defined transformation of thermodynamic and hydrodynamic variables. We argue that this gauge ambiguity is necessary to ascertain the causality of stochastic hydrodynamic evolution and conjecture that it could explain the applicability of hydrodynamics outside its expected regime of validity since far from equilibrium and close to equilibrium may be related through transformations of this type.
A key ingredient of hydrodynamical modeling of relativistic heavy ion collisions is thermal initial conditions, an input that is the consequence of a pre-thermal dynamics which is not completely understood yet. In the paper we employ a recently developed energy-momentum transport model of the pre-thermal stage to study influence of the alternative initial states in nucleus-nucleus collisions on flow and energy density distributions of the matter at the starting time of hydrodynamics. In particular, the dependence of the results on isotropic and anisotropic initial states is analyzed. It is found that at the thermalization time the transverse flow is larger and the maximal energy density is higher for the longitudinally squeezed initial momentum distributions. The results are also sensitive to the relaxation time parameter, equation of state at the thermalization time, and transverse profile of initial energy density distribution: Gaussian approximation, Glauber Monte Carlo profiles, etc. Also, test results ensure that the numerical code based on the energy-momentum transport model is capable of providing both averaged and fluctuating initial conditions for the hydrodynamic simulations of relativistic nuclear collisions.
Recently it has been shown that a realistic description of the medium via event-by-event viscous hydrodynamics plays an important role in the long-standing $R_text{AA}$ vs. $v_2$ puzzle at high $p_T$. In this proceedings we begin to extend this approach to the heavy flavor sector by investigating the effects of full event-by-event fluctuating hydrodynamic backgrounds on the nuclear suppression factor and $v_2{2}$ of heavy flavor mesons and non-photonic electrons at intermediate to high $p_T$. We also show results for $v_3{2}$ of $B^0$ and D$^0$ for PbPb collisions at $sqrt{s}=2.76$ TeV.
Event-by-event viscous hydrodynamics is combined with heavy quark energy loss models to compute heavy flavor flow cumulants $v_2{2}$, $v_3{2}$, and $v_2{4}$ as well as the nuclear modification factors of $D^0$ and $B^0$ mesons in PbPb collisions at 2.76 TeV. Our results indicate that bottom quarks can flow as much as charm quarks in the $p_T$ range 8--30 GeV.
In this lecture note, we present several topics on relativistic hydrodynamics and its application to relativistic heavy ion collisions. In the first part we give a brief introduction to relativistic hydrodynamics in the context of heavy ion collisions. In the second part we present the formalism and some fundamental aspects of relativistic ideal and viscous hydrodynamics. In the third part, we start with some basic checks of the fundamental observables followed by discussion of collective flow, in particular elliptic flow, which is one of the most exciting phenomenon in heavy ion collisions at relativistic energies. Next we discuss how to formulate the hydrodynamic model to describe dynamics of heavy ion collisions. Finally, we conclude the third part of the lecture note by showing some results from ideal hydrodynamic calculations and by comparing them with the experimental data.
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