Excursion amplitude of a Bloch-oscillating wavepacket

For $ϵ(k)={ϵ}_0-2J\cos ka$ and electron force $-eE$, $k(t)=k_0-eEt/\hslash$. Integrating the group velocity gives $x(t)-x(0)=2J[\cos (k_{0}a-{\omega }_{B}t)-\cos (k_{0}a)]/(eE)$, with ${\omega }_B=eEa/\hslash$ for positive $E$. The amplitude about the mean is $2|J|/(e|E|)$ and the peak-to-peak extent is twice that.