Bloch Oscillations: Electron on a Band (2D)

This 2D companion drives the exact same semiclassical tight-binding equations as the 3D version — k(t)=k₀+Et mod 2π, v(k)=2J sin(k) and x(t)=(2J/E)(1−cos(Et)) — through three linked canvas panes instead of an orbiting scene: a lattice strip shows the electron oscillating in real space against a chain of ion cores, a band-diagram pane plots E(k)=−2J cos(k) with a marker riding the curve so the velocity readout is visibly the local slope, and a k-dial sweeps the Brillouin zone and flashes on every Bragg reflection at the zone edge. A free-electron ghost under the identical constant force runs away without limit, making the periodic AC motion of the Bloch electron directly legible against the unbound case.