Algebraic topology and the quantization of circulation in superfluid helium.

Abstract

Onsager's argument for the quantization of circulation in superfluid helium is reconsidered in light of current discussions of quantum mechanics in multiply connected spaces (Aharanov-Bohm effect, fractional statistics, etc.). We find that there is no a priori reason to exclude multiple-valued functions of the order parameter. This results in circulation levels that still exhibit quantized changes of size h/m, but their absolute values are no longer integer multiples of this quantum of circulation. The implications of this theory for experiments using the Vinen vibrating-wire technique are discussed.