Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-07-10
Phys.Rev.D51:5855-5864,1995
Physics
High Energy Physics
High Energy Physics - Theory
26 pages, RevTeX, no figures, published in Phys. Rev. D. 15 May 1995
Scientific paper
10.1103/PhysRevD.51.5855
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 $\nabla\varphi$ 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 $L(\vec s, \nabla\varphi)$ is given by an expression of the form $L=P-3\psi$ where $P$ represents the pressure as a function just of $\nabla\varphi$ 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 $P$.
Carter Brandon
Langlois David
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