Cascade of vortex knots detected by HOMFLYPT polynomial

Abstract eng:
Due to reconnection of neighboring strands superfluid vortex knots seem to undergo a cascade process that consistently reduces topological complexity by stepwise unlinking. Here, by using the HOMFLYPT polynomial recently introduced for fluid knots (Liu & Ricca, 2015), we prove that this cascade process follows a complexity-reducing path detected by a unique, monotonically decreasing sequence of HOMFLYPT numerical values. This result holds true for any sequence of T (2, 2n + 1) torus knots and T (2, 2n) torus links. By this result we demonstrate that the computation of this adapted HOMFLYPT polynomial provides a powerful tool to measure topological complexity of any physical system, and it is useful to investigate relationships between topological complexity and kinetic energy.

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