By Kerson Huang

This attention-grabbing booklet presents the actual and mathematical history for a concept describing the universe as a quantum superfluid, and the way darkish power and darkish topic come up. featuring a singular concept spanning many alternative fields in physics, the foremost suggestions in every one box are introduced.The reader is just anticipated to grasp the rudiments of condensed topic physics, quantum box idea and normal relativity to discover this attention-grabbing new version of darkish subject and darkish strength as elements of a cosmic superfluid.

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**Example text**

1. Here, we want to generalize the variables to the relativistic case, and reformulate the action in terms of them. 16) where V = dV/d(φ∗ φ). The vortex line is a space curve that sweeps out a world sheet in 4D spacetime. The dynamics of the vortex line is therefore that of a relativistic string, which has been widely discussed in the literature [15, 16]. We summarize very brieﬂy how to pass from ﬁeld theory describing the order parameter to string theory describing relativistic vorticity, omitting derivations.

1, ed. C. J. 17. [3] D. Lathrop, Phys. Today, 3 June, 2010. [4] G. D. Holman, Phys. Today, 65, 56 (2012). [5] J. Koplik and H. Levine, Phys. Rev. Lett. 71, 1375 (1993). [6] D. Kivotides, C. F. Barenghi, D. C. Samuels, Phys. Rev. Lett. 87, 155301 (2001). [7] J. Maurer and P. Tabeling, Europhys. Lett. 43, 29 (1998). [8] S. R. Stalp, L. Skrbek, R. J. Donnelly, Phys. Rev. Lett. 82, 4831 (1999). [9] M. Kobayashi and M. Tsubota, Phys. Rev. Lett. 38, 2398 (1988). [10] K. Huang, Lectures on Statistical Physics and Protein Folding (World Scentiﬁc Publishing, Singapore, 2005), Chap.

Com by LA TROBE UNIVERSITY on 10/29/16. For personal use only. Acoustical branch k 0 k0 = 2π/L0 Fig. 2 The Goldstone modes with ω = ck are split into “optical” and “acoustical” branches by gravity. The order parameter will clump into patches of size L0 ; but under present conditions in the universe, L0 is much larger than the radius of the universe. 6 Non-relativistic limit In the non-relativistic limit, φ has a large frequency ω corresponding to σ = ωt. This gives a mass scale mc2 = h¯ ω. The relativistic ﬁeld contains both signs of the frequency: φ = e−iωt Ψ+ + eiωt Ψ− , and the second term can be neglected when ω is large.