Quantized Particle Motion in High Magnetic Fields

Abstract

Recently the dynamics of charged particles in an electric field was discussed from a novel point of view by investigating the evolution of the characteristic structure of the phase η(x,y,...) of the wave functions ψ(x,y,..) = ∣ψ(x,y,..)∣exp(iη(x,y,..) [1]. It was shown for a wide class of Hamiltonians, that this structure behaves according to general laws. In the presence of disorder these laws can change dramatically leading to entirely non-classical particle dynamics. This has been illustrated in the case of one-dimensional conductance without magnetic field [1]. In the present paper we show that analogous nonclassical behaviour is possible in high magnetic fields. We give an example of a two-dimensional system, where disorder leads to quantized, discontinuous motion of particles between distinct sites. This may give new insight into the mechanisms of Hall conductance in disordered systems.