Classical trajectories of ten particles with random initial conditions in the central potential well

Figure 5. Classical trajectories of ten particles with random initial conditions in the central potential well. Parameters are vx = vy = 0.5, B = 0.02, Fy = 0.02 and Fx = 0.

Abstract

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.