Research

My research is mainly under three areas:

Publication

The paper is in Postscript format and has been compressed by gzip.

Thesis

Here is a my Ph.D. thesis in Postscript format.

Multiple Scattering Theory

Inverse Scattering

My research in multiple scattering theory is motivated by the Quatum Corral experiment and its theoretical model by Crommie, Eigler, and Heller (my advisor). Such experiment provides a boundary condition with a movable point source (the STM tip) and known scatterers locations. For S-wave scatterers and for special scatterers with just one angular momentum channel, one can actually obtain the whole scattering T-matrix from the one-tip STM data. In other words, the two-tip STM results can be deduced from the single tip experiment.

Step Edge

Moreover, scattering off a step edge has been investigated. Using a model with an infinite wall, the scattering properties of any step edge can be found by gauging it with Fe adatoms, whose scattering t-matrix is known. And once the scattering properties of the step is known, the total T-matrix of a configuration including the step edge can be found. In other words, the two-tip STM results with the step edge and s-wave scatterers can also be obtained from solely the one-tip data too.

Proximity Resonance

 When two scattererers are placed within their respective Quantum cross section but still outside of their physical cross section, something funny can happens. This is proximity resonance. The wave can be trapped in-between the two scatterers for a long long time before it finally goes away. Proximity Resonance results similar to Heller's 3D results are reproduced in 2D. Moreover, atomic walls of finite length has been studied.

Coherent Backscattering

 Jordan Katine of the Westervelt group has built structures on AlGaAs/GaAs heterostrutures to observe coherent backscattering. In the presence of a perpendicular magnetic field, the resistance is expected to exhibit Aharonv-Bohm-like oscillations. However, only a shoulder reminiscent of the expected peak appears at the correct B-field. This could be attributed to the physical size of the reflectors as well as the presence of impurities in 2DEG. A model has been built with both the boundary wall method as the mathematical hard walls and S-wave scatterers as impurities.
schan@typhoon.harvard.edu
Last modified: Sat Oct 4 17:23:51 EST 1997