<!--HTML-->In small colliding systems and near the QCD critical point, the effects due to hydrodynamic fluctuations can be significant. The effective field theory of fluctuating hydrodynamics has recently been formulated on the closed time path (Schwinger-Keldysh formalism) [1]. Such formulation allows for a systematic treatment of non-linear interaction among energy-momentum densities and hydrodynamics noise. We present the first complete leading order analysis of the effects of hydrodynamic fluctuations on stress-energy tensor correlations and show how those fluctuations modify the dispersion of sound and shear modes. We find the contributions of hydrodynamic fluctuations are parametrically more important than those from the second-order terms in hydrodynamics. We discuss the potential implications of our results for heavy-ion collision phenomenology [2]. [1] M. Crossley, P. Glorioso, and H. Liu, Effective field theory of dissipative fluids, JHEP 1709 (2017) 09. [2] P.H.C. Lau, H. Liu and Y. Yin, in preparation.
<!--HTML-->In small colliding systems and near the QCD critical point, the effects due to hydrodynamic fluctuations can be significant. The effective field theory of fluctuating hydrodynamics has recently been formulated on the closed time path (Schwinger-Keldysh formalism) [1]. Such formulation allows for a systematic treatment of non-linear interaction among energy-momentum densities and hydrodynamics noise. We present the first complete leading order analysis of the effects of hydrodynamic fluctuations on stress-energy tensor correlations and show how those fluctuations modify the dispersion of sound and shear modes. We find the contributions of hydrodynamic fluctuations are parametrically more important than those from the second-order terms in hydrodynamics. We discuss the potential implications of our results for heavy-ion collision phenomenology [2]. [1] M. Crossley, P. Glorioso, and H. Liu, Effective field theory of dissipative fluids, JHEP 1709 (2017) 09. [2] P.H.C. Lau, H. Liu and Y. Yin, in preparation.
We consider nonequilibrium evolution of non-Gaussian fluctuations within relativistic hydrodynamics relevant for the QCD critical point search in heavy-ion collision experiments. We rely on the hierarchy of relaxation timescales, which emerges in the hydrodynamic regime near the critical point, to focus on the slowest mode such as the fluctuations of specific entropy, whose equilibrium magnitude, non-Gaussianity, and typical relaxation time are increasing as the critical point is approached. We derive evolution equations for the non-Gaussian correlators of this diffusive mode in an arbitrary relativistic hydrodynamic flow. We compare with the simpler case of the stochastic diffusion on a static homogeneous background and identify terms which are specific to the case of the full hydrodynamics with pressure fluctuations and flow.
We construct a quantum Schwinger-Keldysh (SK) effective field theory for the diffusive hydrodynamics of a conserved scalar field. Quantum corrections within the SK framework are guided by fluctuation-dissipation relations, enforced via a dynamical Kubo-Martin-Schwinger (KMS) symmetry. We find that the KMS symmetry necessarily generates fluctuation contributions in the SK effective action at all orders in the noise field, thereby giving rise to intrinsically non-Gaussian noise. We use our results to compute one-loop quantum corrections to the two-point density-density retarded correlation function, leading to a quantum generalization of hydrodynamic long-time tails. Our results apply at arbitrarily high orders in ℏ. The one-loop results for retarded correlation functions have been expressed in terms of a family of polynomials. We also provide a closed-form expression for the one-loop results at leading order in the wavevector expansion.
We develop an effective field theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a "fluid spacetime" and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional Z2 symmetry, to which we refer as the local KMS condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, and a higher derivative deformation of supersymmetry in the full quantum regime.
A bstract The search for the conjectured QCD critical point in heavy-ion collisions requires to account for far-from equilibrium effects as well as fluctuations, and in particular non-Gaussian fluctuations, in the modeling of the dynamics of the hot and dense matter created in such collisions. In order to study far-from equilibrium effects as well as fluctuations, in this work we construct a Schwinger-Keldysh effective field theory (EFT) for the diffusion of the density to all orders in derivatives. The dissipation in the free part of our EFT follows the Boltzmann equation in the relaxation-time approximation (RTA). The interaction part of the EFT is constructed based on the self-interaction of the density field. We analytically find the quadratic and cubic parts of the KMS-invariant EFT in closed form, resummed in derivatives. We then explicitly compute the symmetrized three-point function at tree level, and investigate its analytical structure in detail. We also analytically calculate the branch-point singularity that appears in the structure of the two-point response function due to loop effects. Our results are important for future studies of the real-time dynamics of the correlation functions and the possible relation to thermalization when the system is far from equilibrium.
The search for the conjectured QCD critical point in heavy-ion collisions requires to account for far-from equilibrium effects as well as fluctuations, and in particular non-Gaussian fluctuations, in the modeling of the dynamics of the hot and dense matter created in such collisions. In order to study far-from equilibrium effects as well as fluctuations, in this work we construct a Schwinger-Keldysh effective field theory (EFT) for the diffusion of the density to all orders in derivatives. The dissipation in the free part of our EFT follows the Boltzmann equation in the relaxation-time approximation (RTA). The interaction part of the EFT is constructed based on the self-interaction of the density field. We analytically find the quadratic and cubic parts of the KMS-invariant EFT in closed form, resummed in derivatives. We then explicitly compute the symmetrized three-point function at tree level, and investigate its analytical structure in detail. We also analytically calculate the branch-point singularity that appears in the structure of the two-point response function due to loop effects. Our results are important for future studies of the real-time dynamics of the correlation functions and the possible relation to thermalization when the system is far from equilibrium.
The search for the conjectured QCD critical point in heavy-ion collisions requires to account for far-from equilibrium effects as well as fluctuations, and in particular non-Gaussian fluctuations, in the modeling of the dynamics of the hot and dense matter created in such collisions. In order to study far-from equilibrium effects as well as fluctuations, in this work we construct a Schwinger-Keldysh effective field theory (EFT) for the diffusion of the density to all orders in derivatives. The dissipation in the free part of our EFT follows the Boltzmann equation in the relaxation-time approximation (RTA). The interaction part of the EFT is constructed based on the self-interaction of the density field. We analytically find the quadratic and cubic parts of the KMS-invariant EFT in closed form, resummed in derivatives. We then explicitly compute the symmetrized three-point function at tree level, and investigate its analytical structure in detail. We also analytically calculate the branch-point singularity that appears in the structure of the two-point response function due to loop effects. Our results are important for future studies of the real-time dynamics of the correlation functions and the possible relation to thermalization when the system is far from equilibrium.