The projection (8) on the subspace spanned by the ground Wannier states for <em>F</em> = 0 (solid line) and <em>F</em> = 0.015 (dashed line)

<p><strong>Figure 3.</strong> The projection (<a href="http://iopscience.iop.org/0953-4075/46/14/145302/article#jpb466470eqn08" target="_blank">8</a>) on the subspace spanned by the ground Wannier states for <em>F</em> = 0 (solid line) and <em>F</em> = 0.015 (dashed line). The dash-dotted line shows the decrease of total probability in the case <em>F</em> = 0.015 due to absorbing boundary conditions.</p> <p><strong>Abstract</strong></p> <p>We analyse dynamics of a quantum particle in a square lattice in the Hall configuration beyond the single-band approximation. For vanishing gauge (magnetic) field this dynamics is defined by the inter-band Landau–Zener tunnelling, which is responsible for the phenomenon known as the electric breakdown. We show that in the presence of a gauge field this phenomenon is absent, at least, in its common sense. Instead, the Landau–Zener tunnelling leads to the appearance of a finite current which flows in the direction orthogonal to the vector of a potential (electric) field.</p>