Equilibrium thermodynamic susceptibilities for a dense degenerate Dirac field

Abstract

Parity preserving relativistic fluids in four spacetime dimensions admit seven independent thermodynamic susceptibilities at the second order in the hydrodynamic derivative expansion. We compute all parity-even second order thermodynamic susceptibilities for a free massive Dirac field at zero temperature and a nonzero chemical potential, based on the Kubo formulas reported in P. Kovtun and A. Shukla, Kubo formulas for thermodynamic transport coefficients, J. High Energy Phys. 10 (2018) 007. We also compute the second order constitutive relations for the energy-momentum tensor and the conserved current in the absence of external gauge fields.

10 pages, 7 figures. v2: Minor typo fixed. v3: Minor presentation improvements; matches version published in PRD

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• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Cold Quark Matter
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• Thermodynamical second-order hydrodynamic coefficients
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• Kubo formulas for thermodynamic transport coefficients
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• Determining all thermodynamic transport coefficients for an interacting large N quantum field theory
• On the Gravitational Wave to Matter Coupling of Superfluid Fermi Gases Near Unitarity
• Hydrodynamic fluctuations and long-time tails in a fluid on an anisotropic background
• Hydrodynamics in the Carrollian regime
• Gravito-thermal transports, Onsager reciprocal relation and gravitational Wiedemann-Franz law
• Gravitational susceptibility of QGP