Most of the lectures in these proceedings discuss the conductivity of classical resistor networks, in which basic resistors are present (with concentration p) or absent (with concentration 1-p)). The conductivity becomes finite above the geometrical percolation threshold, pc, as soon as there exists an infinite cluster, and its properties are uniquely determined by the geometry of the backbone of this cluster. Both of these aspects change when one considers a quantum particle, whose wave function obeys the Schrodinger equation. Since the wave function may vanish on many sites on the infinite cluster, due to interference effects, the quantum threshold pq turns out to be higher than pc. Quantum conductance also depends drastically on dangling (“dead end”) bonds: a wave may be totally reflected by such bonds, yielding no conductance between the two ends of the sample. Quantitatively, these effects imply localization of all the electronic wave functions up to pq.
KeywordsWave Function Quantum Particle Schrodinger Equation Quantum Hall Effect Basic Resistor
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