rotate_time Subroutine

    subroutine rotate_time()
        implicit none
        ! to avoid code multiplication
        if (t_rotated_time) then
            tau_imag = -sin(real_time_info%time_angle) * tau
            tau_real = cos(real_time_info%time_angle) * tau
        else
            tau_imag = 0.0_dp
            tau_real = tau
        end if
    end subroutine rotate_time