Path-integral expressions of periodic systems are formulated by introducing the concept of the winding number. Computer simulations and a high-temperature expansion demonstrate the quantum effect of the winding number. We then examine the effects of the winding number on the angular and radial distribution functions in two-dimensional polar coordinates both analytically and numerically.

• Received 14 June 1993

DOI:https://doi.org/10.1103/PhysRevE.49.882