Geometric and nongeometric effects in an unbounded mechanical system

An extension of a model proposed by Wilczek and Zee [Phys. Rev. Lett. 52, 2111 (1984)] is studied in this paper. It is shown that slow variation of an adiabatic parameter causes both geometric and nongeometric (i.e., rate dependent) effects in the model that do not vanish in the adiabatic limit. The latter effect is due to the fact that small perturbations of order ε may accumulate over the period of +ε[0,1/ε] if motion of the system is unbounded. Interesting relations between these two effects are discussed. © 1996 The American Physical Society.