Upper panel: participation ratio (7) as functions of time for the parameters of figure 1

<p><strong>Figure 2.</strong> Upper panel: participation ratio (<a href="http://iopscience.iop.org/0953-4075/46/14/145302/article#jpb466470eqn07" target="_blank">7</a>) as functions of time for the parameters of figure <a href="http://iopscience.iop.org/0953-4075/46/14/145302/article#jpb466470f1" target="_blank">1</a>. Lower panel: the same yet <em>F</em> = 0.015, F_x/F_y=(\sqrt{5}-1)/4\approx 0.309. Dashed lines show the participation ratio calculated by using the tight-binding model.</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>