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Effective field theory of dissipative fluids. (English) Zbl 1382.81199
Summary: 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 \(Z_2\) 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.

MSC:
81T60 Supersymmetric field theories in quantum mechanics
82B10 Quantum equilibrium statistical mechanics (general)
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
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