Recent advances in high resolution scanning tunneling spectroscopy of disordered two-dimensional electron systems under high magnetic field will be the starting point for theoretical developments aiming at a quantum description of guiding center motion of the usual cyclotron orbits. The emphasis will be put on real-space imaging of Landau states and the description of some new observables, such as two-point correlations of density of states in the quantum Hall regime. In a second part of the talk, macroscopic transport will be studied theoretically in a high temperature range where the classical percolation of drift states dominates. Crossover functions are obtained, which allow the extraction of critical exponent from recent conductivity measurements.
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