= Bloch oscillation
{c}
In a single isolated <energy band>, a <wave packet> subject to a constant force satisfies $\hbar\dot k=F$. Its <group velocity> is periodic in $k$ with reciprocal-lattice period $2\pi/a$, so its position oscillates with period $2\pi\hbar/(|F|a)$ when its mean velocity over a band is zero. For $E(k)=E_0-2J\cos ka$, integrating the sinusoidal velocity gives the oscillation explicitly. This ideal description neglects scattering and interband tunnelling.
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