Geometric current Jg and its bounds as functions of the frequency ω = 2π/T0. We set that k(t) = k is a constant, r(t) = 0.2 × [sin(ωt) + cos(ωt)], and k (R) (t)/k = 0.5 × (1 + 0.8 × sin(ωt − 0.6π)). The red line (bound 1) denotes the bound (60) with Eq. (58) and the blue line (bound 2) denotes that with Eq. (59). We also show the trivial bound |Jg| ≤ 1 T 0

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... show a numerical result in Fig. 5. The bound in Eq. (58) is basically an increasing function with respect to the frequency ω = 2π/T 0 . As a result the bound becomes loose when we increase ω. On the other hand, it gives a finite contribution at ω → 0. Since the geometric current is known to vanish at the limit, the bound 1 cannot be a good approximation to the ...