TOPOLOGICAL QUANTUM NUMBERS IN NONRELATIVISTIC PHYSICS

Voltage measurements using the ac Josephson effect and electrical resi stance 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 He-4, flux quantization in superconductors and quantized Hall conductance are all examples of topological quantum numbers, but only the last two are kn own to be very precise. Vinen's early measurement of quantized circula tion was based on measurement of the resulting Magnus force, and we (P ing Ao, Qian Niu and I) have recently shown that the strength of the M agnus force can itself be determined by an argument that shares common features with topological arguments.