Abstract
Developing on a recent work on localized bubbles of ordinary relativistic fluids, we study the comparatively richer leading order surface physics of relativistic superfluids, coupled to an arbitrary stationary background metric and gauge field in 3 + 1 and 2 + 1 dimensions. The analysis is performed with the help of a Euclidean effective action in one lower dimension, written in terms of the superfluid Goldstone mode, the shape-field (characterizing the surface of the superfluid bubble) and the background fields. We find new terms in the ideal order constitutive relations of the superfluid surface, in both the parity-even and parity-odd sectors, with the corresponding transport coefficients entirely fixed in terms of the first order bulk transport coefficients. Some bulk transport coefficients even enter and modify the surface thermodynamics. In the process, we also evaluate the stationary first order parity-odd bulk currents in 2 + 1 dimensions, which follows from four independent terms in the superfluid effective action in that sector. In the second part of the paper, we extend our analysis to stationary surfaces in 3 + 1 dimensional Galilean superfluids via the null reduction of null superfluids in 4 + 1 dimensions. The ideal order constitutive relations in the Galilean case also exhibit some new terms similar to their relativistic counterparts. Finally, in the relativistic context, we turn on slow but arbitrary time dependence and answer some of the key questions regarding the time-dependent dynamics of the shape-field using the second law of thermodynamics. A linearized fluctuation analysis in 2 + 1 dimensions about a toy equilibrium configuration reveals some new surface modes, including parity-odd ones. Our framework can be easily applied to model more general interfaces between distinct fluid-phases.
Highlights
QuantitiesGμν, (G = det Gμν ), ∇μAμ, Fμν = ∂μAν − ∂ν Aμ ǫμν ρσ : ǫ0123√1 −G (3+1), ǫμνρ: ǫ012 = (2+1)Superfluid Quantities uμ with uμuμ = −1 T, μ, (ν = μ/T )φ, ξμ = −∂μφ + Aμ, (ζμ = ξμ +uμ)χ = −ξμξμ, χ = −ζμζμ f, Gμν −nμnν, nμ ∇ ̃ μ(· √1 ∇ν f ∇ν f ∂μf ··)
We find new terms in the ideal order constitutive relations of the superfluid surface, in both the parity-even and parity-odd sectors, with the corresponding transport coefficients entirely fixed in terms of the first order bulk transport coefficients
We find that the ideal order surface currents receive contributions from the bulk transport coefficients leading to different thermodynamics compared to the bulk
Summary
To begin with, following [8], we shall mainly focus on stationary relativistic superfluid bubbles, which will enable us to employ the partition function techniques discussed in [11,12,13]. We will obtain the surface currents in (1.10) in a special hydrodynamic frame, which is the frame that follows directly from equilibrium partition functions In this frame, defining K = ∂t as the time-like Killing vector field of the background, the usual ordinary fluid variables are given by. This prompts us to include a dependence of the interface partition function S(s) on the superfluid velocity In this context, it is worthwhile pointing out that expanding around the background interpolating profile of ψ, and keeping terms up to the quadratic order in φ, we see that S(s) can depend on the magnitude of the superfluid velocity, as well as on its component along the direction normal to the surface, both being Lorentz scalars from the interface point of view. In 2 + 1 and 3 + 1 dimensions respectively. 12In the presence of surfaces, the effect of such φ shifts at the surface can be absorbed by a redefinition of the surface partition function. 13Note that these terms are the parity-odd first order corrections on the surface of the 3 + 1 dimensional superfluid bubble
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
