The Kibble-Zurek mechanism in helium-4?

Mathematics – Logic

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Scientific paper

When a physical system passes rapidly through a 2nd order (continuous) phase transition, the creation of topological defects is to be anticipated [1] at a density that depends on the speed with which the transition is traversed [2]. This Kibble-Zurek (K-Z) mechanism must in principle operate during any 2nd order phase transition, but it is of particular interest in relation to the grand unified theory (GUT) symmetry-breaking phase transition of the early universe, ~10-35 s after the Big Bang. Just after the transition at ~1027K, the nascent new phase of the vacuum is disordered and gives rise to a variety of topological defects. These include cosmic strings, which may represent the primordial density inhomogeneities that later gave rise to galaxy formation. The GUT phase transition occurred at such high energy (temperature) that it cannot be reproduced. The only feasible experimental test is to study analogous phase transitions in systems that are accessible in the laboratory. These have included liquid crystals, liquid 4He [3,4], liquid 3He, and Josephson tunnel junctions. Most of the experiments apparently produce results consistent with the K-Z predictions -- but, mysteriously, not (so far) liquid 4He which was the subject of Zurek's original [2] proposal for a cosmological experiment. Superfluid 4He is described by a complex macroscopic order parameter (condensate wave function) whose real and imaginary parts play the role of Higgs fields. Possible reasons for an unexpectedly null result [4], and new experiments now in progress, will be discussed.
References
[1] T W B Kibble, J. Phys. A 9, 1387 (1976).
[2] W H Zurek, Nature 317, 505 (1985).
[3] P C Hendry, N S Lawson, R A M Lee, P V E McClintock and C D H Williams, Nature 368, 315 (1994).
[4] M E Dodd, P C Hendry, N S Lawson, P V E McClintock and C D H Williams, Phys. Rev. Lett. 81, 3703 (1998).

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