Topological Quantum Numbers in Nonrelativistic Physics
Voltage measurements using the ac Josephson effect and electrical resistance measurements using the quantum Hall effect are capable of very high precision, despite the relatively poor control of details of the devices. Such measurements rely on topological quantum numbers, which, unlike symmetry-based quantum numbers, are insensitive to deviations of the system from ideality. The circulation in superfluid 4He, flux quantization in superconductors and quantized Hall conductance are all examples of topological quantum numbers, but only the last two are known to be very precise. Vinen's early measurement of quantized circulation was based on measurement of the resulting Magnus force, and we (Ping Ao, Qian Niu and I) have recently shown that the strength of the Magnus force can itself be determined by an argument that shares common features with topological arguments.