= Solution
In an isolated <energy band>, semiclassical motion satisfies $\hbar\dot k=F$ and $v=\hbar^{-1}dE/dk$. The band is periodic in <crystal momentum>, so a constant force sweeps the state through equivalent points of the <Brillouin zone>. Its velocity repeats rather than increasing without bound. For an electron in a constant <electric field>, $F=-e\mathcal E$, and the <Bloch oscillation> period is
$$
\boxed{T_B=\frac{2\pi\hbar}{e|\mathcal E|a},\qquad\omega_B=\frac{e|\mathcal E|a}{\hbar}.}
$$
For $E(k)=E_0-2J\cos ka$, $v=(2Ja/\hbar)\sin ka$ and integration gives a bounded position oscillation of amplitude $2J/|F|$ about its mean. A filled band has no corresponding net transport oscillation after summing uniformly over all $k$.
Observation requires scattering times longer than $T_B$ and negligible <interband tunnelling>. Ordinary crystals often scatter too rapidly before a full zone traversal; larger-period structures and clean atom-optical lattices help. In the <cold-atom Bloch oscillation experiment>, accelerating a standing-wave lattice supplied a controlled force, and releasing the atoms at different times revealed an oscillating momentum distribution.<Bloch Oscillations of Atoms in an Optical Potential by Maxime Dahan and others>[Physical Review Letters 76, 4508–4511 (1996), lattice acceleration and momentum measurements]{ref}
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