Fractional statistics and analogs of quantum Hall effect in superfluid 3He films

Abstract

The superfluid 3He phases provide us with systems which share many of the properties of the physical vacuum in particle physics including bosons, fermions, gauge fields, gravity, chiral anomaly, zero‐charge effect, etc. The superfluid phases which may exist in thin 3He films have additional properties of a two‐dimensional origin, such as the fractionally quantized Hall conductivity. This quantum Hall effect (QHE) is representative of a whole class of phenomena caused by the quantization of physical parameters. They include fractional charge and spin of the particle‐like solitons in superfluid 3He films on QHE for spin current. All quantized physical parameters (charge, spin, Hall conductivity) have step‐like dependence on the film thickness. Also the quantum statistics of solitons changes with film thickness, alternating between Fermi‐, Bose‐ and possibly parastatistics.