Vortex formation and dynamics in superfluid 3He and analogies in quantum field theory

Abstract

The formation and dynamics of topological defects of different structure has been of central interest in the study of the 3 He superfluids. Compared to superfluid 4 He-II, the variability of the important parameters with temperature and pressure is wider and many features are more ideal. This has made experimentally new approaches possible. An example is the formation of quantized vortices and other topological defects in a rapid time-dependent phase transition from the normal state to 3 He-B. This vortex formation process is known as the Kibble-Zurek mechanism and is one the central topics of this review. It demonstrates the use 3 He-B as a model system for quantum fields, with detailed control from the laboratory.PACS: 67.57. Fg, 47.32, 05.70.Fh, 98.80.Cq.

Weak turbulence of Kelvin waves in superfluid He

“…Then the energy is transferred through the crossover scale by some complicated mechanisms [17][18][19], thereby exciting smaller scales < < a λ which propagate along the individual vortex filaments as waves. These were predicted by Lord Kelvin more than one century ago [12] and experimentally observed in superfluid 4 He about 50 years ago. It is believed that Kelvin waves (KWs) play a crucial role in superfluid dynamics, transferring energy from to a much smaller scale, where it can dissipate via emission of bulk phonons.…”

“…There are four of them. The first one originates from the region where 1 k and 2 k are much smaller than the rest of ' j k s. The three other contributions originate from the other side of the sextet: regions where either 3 k and 4 , k or 3 k and 5 k , or 4 k and 5 k are small. These contributions are equal and we may find only one of them and multiply the result by three.…”

“…In superfluids, on the other hand, when temperature is close to the absolute zero, such quenching mechanism is absent, and the energy flux unavoidably reaches the scales where the quantization of the vortex circulation (discovered by Feynman [3]) is essential. Recently, there have been significant advances in experimental techniques allowing studies of turbulence in various systems such as 3 He [4,5], 4 He [6,7] and Bose-Einstein condensates of supercold atoms [8,9]. Often, experimental devices are not small enough to probe the transitional and quantum scales directly.…”

“…For the six-wave process, which assumes that the underlying vortex is perfectly straight, this task was accomplished only recently [14]. Effective 3↔3-interaction coefficient W was shown to have a form 4,5,6 4,5,6 1 2 3 4 5 6 1,2,3 1,2,3…”

“…x Note that all the similar integrals over 2 , k 3 , k 4 , k and 5 k in Eq. (9) also diverge exactly in the same manner as integral (16).…”