Dynamical spectral structure of density fluctuation near QCD critical point

The expression for the dynamical spectral structure of the density fluctuation near the QCD critical point has been derived using linear response theory within the purview of Israel-Stewart relativistic viscous hydrodynamics. The change in spectral structure of the system as it moves toward critical end point has been studied. The effects of the critical point have been introduced in the system through a realistic equation of state and the scaling behaviour of various transport coefficients and thermodynamic response functions. We have found that the Brillouin and the Rayleigh peaks are distinctly visible when the system is away from critical point but the peaks tend to merge near the critical point. The sensitivity of structure of the spectral function on wave vector ($k$) of the sound wave has been demonstrated. It has been shown that the Brillouin peaks get merged with the Rayleigh peak because of the absorption of sound waves in the vicinity of the critical point.