Vortex lines in superfluids are characterized by their quantised circulation: $k = \frac{h}{m}\times n$, where $n$ is the winding number in the sense of a topological winding number. Now, most vortex lines want to be $n=1$ as this is the lowest energy state, but this raises a question that my supervisor couldn't answer: can vortex lines bifurcate? We want this answer to be yes, but I have read that there is no way to continuously deform a winding number of $n$ into $m$ where $n$ is not equal to $m$. However, is this also true for the case where, say, $n=2$ and $m=2\times 1$? i.e. we have this bifurcation I mentioned.

  • $\begingroup$ Could you explain what you mean by bifurcate in this context? $\endgroup$ – octonion Oct 15 '19 at 7:53
  • $\begingroup$ If you are talking about a vortex with $n>1$ splitting up into many $n=1$ vortices, yes that is allowed and usually more stable $\endgroup$ – octonion Oct 15 '19 at 7:56
  • $\begingroup$ Yes that's exactly it thankyou. $\endgroup$ – Jack Hughes Oct 15 '19 at 12:33

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