Impurities, lattice imperfections, and other forms of disorder crucially affect properties of electronic and other materials. Disorder alone can prevent electric current from flowing, turning a metal into an insulator. This is a consequence of the wave nature of the electron and the interference of electron waves scattered by impurities.
Read Scaling Phenomena In Disordered Systems
The PI will use sophisticated theoretical concepts and mathematical methods to advance understanding of this transformation between a metal and an insulator as the amount of disorder is varied. The PI will also study how this transformation takes place in a quantum Hall system where electron conduction is richly complex.
A quantum Hall system is a gas of electrons confined to a plane in an artificial semiconductor structure with an applied magnetic field perpendicular to the plane. The conduction of electrons through a quantum Hall system varies in interesting ways depending on the strength of the magnetic field.
Of particular interest is the effect of the interplay of the magnetic field with disorder on the conduction of electrons through a quantum Hall system.
The PI will also use sophisticated mathematical methods to advance understanding of random patterns that arise in growth. Examples of such patterns are evident in soot particles, bacterial colonies grown in a Petri dish, fingered patterns of minerals deposited by water seeping through porous rock, and vortices in turbulent fluid flows. The shapes that arise are generally rough and fractal - when examined more closely, a magnified image looks the same as the unaided image. These fractals are often driven by random forces, requiring their characterization in terms of probabilities.
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