Bodo Huckestein

Scaling theory of the integer quantum Hall effect

A brief review is given of the present understanding of the transitions between integer quantized plateaus of the Hall conductivity in two-dimensional disordered systems in a strong magnetic field. The similarity to continuous thermodynamic phase transitions is emphasized. Results of numerical simulations for non-interacting electrons are presented and compared to experiment. The role of the Coulomb interactions at the integer quantum Hall transitions is studied.

Quantum hall effect at low magnetic fields

The temperature and scale dependence of resistivities in the standard scaling theory of the integer quantum Hall effect is discussed. It is shown that recent experiments, claiming to observe a discrepancy with the global phase diagram of the quantum Hall effect, are in fact in agreement with the standard theory. The apparent low-field transition observed in the experiments is identified as a crossover due to weak localization and a strong reduction of the conductivity when Landau quantization becomes dominant.

Relation between the correlation dimensions of multifractal wave functions and spectral measures in integer quantum Hall systems.

We study the time evolution of wavepackets of non-interacting electrons in a two-dimensional disordered system in strong magnetic field. For wavepackets built from states near the metal-insulator transition in the center of the lowest Landau band we find that the return probability to the origin

Quantum transport through ballistic cavities: soft vs. hard quantum chaos

p(t)

CORRECTIONS TO SCALING IN THE INTEGER QUANTUM HALL EFFECT

decays algebraically,

Fractal Conductance Fluctuations in Gold Nanowires.

p(t) \sim t^{-D_2/2}

Interactions, localization, and the integer quantum hall effect

, with a non-conventional exponent

INTEGER QUANTUM HALL EFFECT OF INTERACTING ELECTRONS : DYNAMICAL SCALING AND CRITICAL CONDUCTIVITY

D_2/2

Spatial and spectral multifractality of the local density of states at the mobility edge

.

NETWORK MODEL FOR A TWO-DIMENSIONAL DISORDERED ELECTRON SYSTEM WITH SPIN-ORBIT SCATTERING

D_2