Fig. 1
Time evolution of the geometric phase for several different values of A0. The values of (μ, ν) used in the graphics are (1, 0) for a, (\(\sqrt {2}\), 1) for b, and (\(\sqrt {3}\), \(\sqrt {2}\)) for c. We have used m=1, ω0=1, ω=5, γ=0.35, fd=1, \(\hbar =1\), φ=0, and γG(0)=0. The phase and all parameters are taken to be dimensionless for convenience, and this convention will also be applied to the subsequent figures. Because A0 is given in terms of the classical amplitude Xc,0 of the complementary function [see Eq. (12)], we can confirm from the graphics that the geometric phase is large when the oscillation amplitude is high. We also see that the fluctuation of γG(t) becomes large as the values μ and ν increase under the condition given in Eq. (14)