Spectrum of Geometric Phases in a Driven Oscillator

We study geometric phases underlying the time evolution of the quantum wave function of a driven nonlinear oscillator exhibiting periodic, quasiperiodic as well as chaotic dynamics. In the asymptotic limit, irrespective of the classical dynamics, the geometric phases are found to increase linearly with time. However, the fingerprints of classical motion are present in the bounded fluctuations that are superimposed on the monotonically growing phases, as well as in the difference in phases between two neighboring quantum states.