Fig. 5

Time evolution of the expectation value \(\langle \psi _{\mathrm{s},n}^\epsilon (t) | {\hat{q}} | \psi _{\mathrm{s},n}^\epsilon (t) \rangle\) for the case that time functions are chosen to be Eqs. (81)–(87). The value of \(\epsilon\) is 1 for (a), \(1+0.005i\) for (b), and \(1+0.02i\) for (c). Other values taken here are \(L=1\), \(C_0 = 1\), \({\textsf {Q}}=1\), \(\omega _{1}=1\), \(\rho _0=1\), \(r =1\), \(\phi =1\), \(Q_{\mathrm{t},c}(0)=1\), \(P_{\mathrm{t},c}(0)=1\), \(\hbar =1\), \(\beta =0.02\), and \(n=1\)