Logarithm of |Ψ(<em>x</em>, <em>y</em>, <em>t</em>)|<sup>2</sup> at <em>t</em> = 10 000 D N Maksimov I Yu Chesnokov D V Makarov A R Kolovsky 10.6084/m9.figshare.1012174.v1 https://iop.figshare.com/articles/figure/_Logarithm_of_em_x_em_em_y_em_em_t_em_sup_2_sup_at_em_t_em_10_000/1012174 <p><strong>Figure 6.</strong> Logarithm of |Ψ(<em>x</em>, <em>y</em>, <em>t</em>)|<sup>2</sup> at <em>t</em> = 10 000. Parameters are <em>v<sub>x</sub></em> = <em>v<sub>y</sub></em> = 0.5, α = 1/8 (<em>B</em> ≈ 0.02), <em>F<sub>y</sub></em> = 0.015 and <em>F<sub>x</sub></em> = 0.</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> 2013-06-13 00:00:00 phenomenon analyse dynamics 0. Abstract quantum particle tunnelling square lattice landau Hall configuration direction orthogonal gauge field Atomic Physics Molecular Physics