Fig. 4

The effects of the electromotive force on the probability density \(|\psi _{\mathrm{s},n}^\epsilon ({q},t)|^2\) [Eq. (41)]. We used the parameters illustrated in Eqs. (81)–(87). The values of parameters \(({\textsf {Q}}, \omega _1)\) associated with the electromotive force are \(({\textsf {Q}}, \omega _1)=(0.5, 5)\) for (a), \(({\textsf {Q}}, \omega _1)=(5, 1.5)\) for (b), and \(({\textsf {Q}}, \omega _1)=(10, 0.5)\) for (c). Other values taken here are \(Q_{\mathrm{t},c}(0)=5\), \(P_{\mathrm{t},c}(0)=5\), \(L=1\), \(C_0 = 1\), \(\omega _0=1\), \(\epsilon =(1+i)/\sqrt{2}\), \(r=1\), \(\phi =1\), \(\hbar =1\), \(\beta =0.1\), and \(n=3\), which, in fact, are the same as those of Fig. 3b