Quantized Particle Motion in High Magnetic Fields
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,..) . 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 . 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.
KeywordsHigh Magnetic Field Hall Conductance Threshold Field Weak Disorder Disorder Potential
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- 2.J. von Neumann and E. Wigner: Phys. Z. 30, 467 (1929)Google Scholar
- 3.See e.g. L. D. Landau and E. M. Lifshitz: In Quantum Mechanics, Course of Theoretical Physics, Vol.3 (Pergamon, London, Paris 1959), sec.76Google Scholar
- 4.See e.g. D. Lenstra and W. van Haeringen, J. Phys. C14, 5293 (1981)Google Scholar