Excursion amplitude of a Bloch-oscillating wavepacket
= Excursion amplitude of a Bloch-oscillating wavepacket
For $\epsilon(k)=\epsilon_0-2J\cos ka$ and electron force $-eE$, $k(t)=k_0-eEt/\hbar$. Integrating the <group velocity> gives $x(t)-x(0)=2J[\cos(k_0a-\omega_Bt)-\cos(k_0a)]/(eE)$, with $\omega_B=eEa/\hbar$ for positive $E$. The amplitude about the mean is $2|J|/(e|E|)$ and the peak-to-peak extent is twice that.