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arXiv · hep-th/9507058

The Equation of State for Cool Relativistic Two-Constituent Superfluid Dynamics

Brandon Carter·David Langlois
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Abstract

The natural relativistic generalisation of Landau's two constituent superfluid theory can be formulated in terms of a Lagrangian $L$ that is given as a function of the entropy current 4-vector $s^ρ$ and the gradient $\nablaφ$ of the superfluid phase scalar. It is shown that in the ``cool" regime, for which the entropy is attributable just to phonons (not rotons), the Lagrangian function $L(\vec s, \nablaφ)$ is given by an expression of the form $L=P-3ψ$ where $P$ represents the pressure as a function just of $\nablaφ$ in the (isotropic) cold limit. The entropy current dependent contribution $ψ$ represents the generalised pressure of the (non-isotropic) phonon gas, which is obtained as the negative of the corresponding grand potential energy per unit volume, whose explicit form has a simple algebraic dependence on the sound or ``phonon" speed $c_P$ that is determined by the cold pressure function $P$.

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Brandon Carter, David Langlois. 1995-07-10. The Equation of State for Cool Relativistic Two-Constituent Superfluid Dynamics. https://doi.org/10.1103/physrevd.51.5855

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