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We develop the relativistic theory of hydrodynamic fluctuations forapplication to high energy heavy ion collisions. In particular, we investigatetheir effect on the expanding boost-invariant (Bjorken) solution of thehydrodynamic equations. We discover that correlations over a long rapidityrange 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 thelimit of zero viscosity. As a result, there is a non-dissipative wake behindthe sound front which is generated by any instantaneous point-like fluctuation.We evaluate the two-particle correlators using the initial conditions andhydrodynamic parameters relevant for heavy-ion collisions at RHIC and LHC. Inprinciple these correlators can be used to obtain information about theviscosities because the magnitudes of the fluctuations are directlyproportional to them.

Relativistic Theory of Hydrodynamic Fluctuations with Applications to Heavy Ion Collisions