Abstract

The quantum behaviour of cold particles confined to two dimensions appears to exhibit peculiar characteristics, arising through the presence of gyroscopic terms in the Lagrangian [1]. A typical example, and one which we treat here as the generic case, is that of a trapped ion in a constant magnetic field. The gyroscopic terms involve cross-products of position and velocity: they are particle-like specialisations of topological Lagrangians, which, under the sobriquet of Chern-Simons, are familiar in odd-dimensional spacetime field-theory.

© 1998 IEEE