**(c) Dr Paul Kinsler.**
[Acknowledgements & Feedback]

Analytic and numerical techniques

Analytic techniques I have used included applications of several complex number representations of quantum electrodynamics, including the well known Wigner representation. These transform the time development equations for the system operator into real or complex number Fokker- Planck equations. The non-linear differential equations that resulted from the system I was describing were also written in their alternative stochastic form. I calculated solutions of both forms of the equations for relevant cases using analytical and numerical techniques. The numerical work primarily involved evaluating both the steady state and dynamical behaviours of the stochastic equations. These results were calculated by Fortran programs I wrote for that purpose.

These were complimented by approaches using standard perturbation theory, as well as eigenvalue calculations based on high dimensional matrix equations that were generated by using the integer number state basis. In addition I made use of computer animated representations of the stochastic simulations, using my own animation software. This was useful for getting an intuitive feel for the dynamics.

I have also used Greens function methods to study the spectral properties of coupled systems. In addition, I have looked at extending the use of quantum mechanical versions of stochastic equations to systems interacting with a common heat bath. These quantum equations are then reduced in the appropriate limits to complex number and real number rate equations to model experimental results.

In order to understand how electrons scatter from confined and interface phonons in semiconductor microstructures I needed to apply the Fermi Golden rule from scratch, which was most enlightening. I have written a Monte Carlo program to simulate electron transport in semiconductor microstructures, for which I needed to learn about the relevant the theory and methods. As I now plan to extend my work to holes, which have a more complicated subband structure, the scattering rate and monte carlo algorithms need to be made more flexible.

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Date=19991109 19981015 Author=P.Kinsler Created=19951114