 Excursion amplitude of a Bloch-oscillating wavepacket

ID: excursion-amplitude-of-a-bloch-oscillating-wavepacket

For

ϵ (k) = ϵ_{0} - 2 J cos ka

- e E

k (t) = k_{0} - e Et /ℏ

. Integrating the group velocity gives

x (t) - x (0) = 2 J [cos (k_{0} a - ω_{B} t) - cos (k_{0} a)] / (e E)

, with

ω_{B} = e E a /ℏ

for positive

E

. The amplitude about the mean is

2∣ J ∣/ (e ∣ E ∣)

and the peak-to-peak extent is twice that.

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