# Superfluid Vortex Lines Bifurcation and Winding Numbers

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.

• Could you explain what you mean by bifurcate in this context? – octonion Oct 15 '19 at 7:53
• 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 – octonion Oct 15 '19 at 7:56
• Yes that's exactly it thankyou. – Jack Hughes Oct 15 '19 at 12:33