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

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 $s^{\rho }$ and the gradient $\nabla \phi$ 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 $L(\vec{s},\nabla \phi )$ is given by an expression of the form $L=P-3\psi$ where $P$ represents the pressure as a function just of $\nabla \phi$ in the (isotropic) cold limit. The entropy current dependent contribution $\psi$ 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 $P$.

26 pages, RevTeX, no figures, published in Phys. Rev. D. 15 May 1995

References in corpus (1)

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