Quantization of the Hall conductance and delocalization in ergodic Landau Hamiltonians

Abstract

We prove quantization of the Hall conductance for continuous ergodic Landau Hamiltonians under a condition on the decay of the Fermi projections. This condition and continuity of the integrated density of states are shown to imply continuity of the Hall conductance. In addition, we prove the existence of delocalization near each Landau level for these two-dimensional Hamiltonians. More precisely, we prove that for some ergodic Landau Hamiltonians there exists an energy $E$ near each Landau level where a ``localization length'' diverges. For the Anderson-Landau Hamiltonian we also obtain a transition between dynamical localization and dynamical delocalization in the Landau bands, with a minimal rate of transport, even in cases when the spectral gaps are closed.

Misprints, updated references

References in corpus (3)

• New characterizations of the region of complete localization for random Schrödinger operators
• Linear response theory for magnetic Schroedinger operators in disordered media
• The absolute continuity of the integrated density of states for magnetic Schrödinger operators with certain unbounded random potentials

Cited by in corpus (11)

• A comprehensive proof of localization for continuous Anderson models with singular random potentials
• Quantization of edge currents along magnetic barriers and magnetic guides
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• Conductivity and the current-current correlation measure
• The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects
• Power law logarithmic bounds of moments for long range operators in arbitrary dimension
• From orbital magnetism to bulk-edge correspondence
• Splitting of the Landau levels by magnetic perturbations and Anderson transition in 2D-random magnetic media
• Random Schrödinger Operators on discrete structures
• Dynamical mobility edge for various random Landau Hamiltonians