\alpha_{\textbf{k}}=u_{\textbf{k}}c^{\phantom{\dagger}}_{\textbf{k},\uparrow}-v_{\textbf{k}}c^{\dagger}_{\textbf{-k},\downarrow}, 
\qquad 
\beta_{\textbf{k}} =v_{\textbf{k}} c^{\dagger}_{\textbf{k},\uparrow}+ u_{\textbf{k}} c^{\phantom{\dagger}}_{-\textbf{k},\downarrow} ,\end{aligned}$$ where $
v_{\textbf{k}}= \Delta (t_i ) / |\Delta (t_i ) | \sqrt{ ( 1 - \epsilon_{\textbf{k}} /  E_{\textbf{k}}   )/2 }
$, $
u_{\textbf{k}}=\sqrt{  ( 1+ \epsilon_{\textbf{k}} /  E_{\textbf{k}}  )/2}
$, and $E_{\textbf{k}}=\sqrt{\epsilon^2_{\textbf{k}}+|\Delta (t_i ) |^2}$. We emphasize that the coefficients $u_{\textbf{k}}$ and $v_{\textbf{k}}$ do not depend on time, i.e., the temporal evolution of the quasiparticle densities is computed with respect to a fixed time-independent Bogoliubov-de Gennes basis in which the initial state is diagonal. All physical observables, such as the electric current density ${\bf j}_{{\bf q}_{\textrm{pr}}} (t)$, the order parameter amplitude $| \Delta (t) |$, and the lattice displacement $U ( {\bf r}, t)$ can now be expressed in terms of the new Bogoliubov quasiparticle densities $\langle\alpha^{\dagger}_{\textbf{k}}\alpha^{\phantom{\dagger}}_{\textbf{k}' } \rangle$, $\langle\beta^{\dagger}_{\textbf{k}}\beta^{\phantom{\dagger}}_{\textbf{k}' } \rangle$, $\langle\alpha^{\dagger}_{\textbf{k}}\beta^{\dagger}_{\textbf{k}' } \rangle$, and $\langle\alpha^{\phantom{\dagger}}_{\textbf{k}}\beta^{\phantom{\dagger}}_{\textbf{k}' } \rangle$. For example, for the current density ${\bf j}_{{\bf q}_{\textrm{pr}}} (t)$ we find $$\begin{aligned}
&& 
{\bf j}_{{\bf q}_{\textrm{pr}}} (t) 
=
\frac{-e\hbar}{2mV}\sum_{\bf k}(2{\bf k}+{\bf q}_{\textrm{pr}})
\\
&&
\; \times
\Big[  
(u_{{\bf k}}v_{{\bf k}+{\bf q}_{\textrm{pr}}}-v_{{\bf k}}u_{{\bf k}+{\bf q}_{\textrm{pr}}})
\big(
\langle\alpha^{\dagger}_{\textbf{k}}\beta^{\dagger}_{{\bf k}+{\bf q}_{\textrm{pr}} } \rangle   
+
\langle \alpha^{\phantom{\dagger}}_{{\bf k}+{\bf q}_{\textrm{pr}} } \beta^{\phantom{\dagger}}_{\textbf{k}} \rangle 
\big)
\nonumber\\
&&
\; +(u_{{\bf k}}u_{{\bf k}+{\bf q}_{\textrm{pr}}}+v_{{\bf k}}v_{{\bf k}+{\bf q}_{\textrm{pr}}}) 
\big(
 \langle\alpha^{\dagger}_{\textbf{k}}\alpha^{\phantom{\dagger}}_{{\bf k}+{\bf 