Viscosity and dissipative hydrodynamics from effective field theory

Grozdanov, Saso and Polónyi, János (2015) Viscosity and dissipative hydrodynamics from effective field theory. PHYSICAL REVIEW D, 91 (10). ISSN 2470-0010

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Abstract

With the goal of deriving dissipative hydrodynamics from an action, we study classical actions foropen systems, which follow from the generic structure of effective actions in the Schwinger-KeldyshClosed-Time-Path formalism with two time axes and a doubling of degrees of freedom. The centralstructural feature of such effective actions is the coupling between degrees of freedom on the two timeaxes. This reflects the fact that from an effective field theory point of view, dissipation is the lossof energy of the low-energy hydrodynamical degrees of freedom to the integrated-out, UV degreesof freedom of the environment. The dynamics of only the hydrodynamical modes may therefore notposses a conserved stress-energy tensor. After a general discussion of the CTP effective actions, weuse the variational principle to derive the energy-momentum balance equation for a dissipative fluidfrom an effective Goldstone action of the long-range hydrodynamical modes. Despite the absence ofconserved energy and momentum, we show that we can construct the first-order dissipative stress-energy tensor and derive the Navier-Stokes equations near hydrodynamical equilibrium. The shearviscosity is shown to vanish in the classical theory under consideration, while the bulk viscosity isdetermined by the form of the effective action. We also discuss the thermodynamics of the systemand analyse the entropy production.

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