Abstract
We develop the relativistic theory of hydrodynamic fluctuations for application to high energy heavy ion collisions. In particular, we investigate their effect on the expanding boost-invariant (Bjorken) solution of the hydrodynamic equations. We discover that correlations over a long rapidity range are induced by the propagation of the sound modes. Due to the expansion, the dispersion law for these modes is non-linear and attenuated even in the limit of zero viscosity. As a result, there is a non-dissipative wake behind the sound front which is generated by any instantaneous point-like fluctuation. We evaluate the two-particle correlators using the initial conditions and hydrodynamic parameters relevant for heavy-ion collisions at RHIC and LHC. In principle these correlators can be used to obtain information about the viscosities because the magnitudes of the fluctuations are directly proportional to them.
Highlights
N We develop the relativististic theory of hydrodynamic fluctuations for application Y O to high energy heavy ion collisions
In this paper we explored the contribution of local hydrodynamic fluctuations to the event-by-event fluctuations of particles emitted from relativistic heavy ion collisions
Unlike the contribution of initial state fluctuations, which have been the main focus of the studies so far and whose magnitude is determined by quantum pre-equilibrium dynamics, the magnitude of the fluctuations we discussed here is directly related to the hydrodynamic properties of the locally equilibrated matter
Summary
Hydrodynamics is an effective theory that describes the long wavelength and low frequency space-time evolution of the densities of a few conserved quantities such as energy, momentum, electric charge and baryon number. In the case of spontaneous breaking of continuous symmetries it describes the evolution of the phases of order parameters. These hydrodynamic variables are defined as average values of the corresponding local, space-time dependent, coarse-grained operators. The fluctuations themselves occur on microscopically short space-time scales, these fluctuations are correlated on short space-time scales and on macroscopically large scales. This can be understood as a result of the diffusion or propagation of each fluctuation at any earlier time to later times. Such propagation over long times and distances, and the long-range behavior of correlation functions, is described by hydrodynamics
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