An Introduction to the Density Matrix in Quantum Mechanics
That abstract is from my B.Sc. thesis (which isn’t publicly available) reads:
Abstract. The first quantum mechanical model of conductivity based on the quantum master equations is developed and used to model the linear response to pulsed THz perturbation. It gives an explanation to the non-Drude-like behavior in the nanoregime and shows Drude-like models to be a limiting case as materials approach a bulk structure. It is shown that chirp as well as pulse duration affect the frequency-window, that can be probed theoretically. The theory is expanded to consider the Fermi-Dirac statistic as well as N-level systems and the influence of the domain size, temperature, dephasing and relaxation mechanisms are discussed in detail. The theory fully explains the oscillations in the THz spectrum of CdSe semiconductor nanorods. Yet, it is not limited to it but general enough to be adapted to different kinds of materials and geometries. It can be expanded further to also consider non-linear effects as it is beyond the need of analytical solutions.
Reading my own abstract again, I am cringing to be honest. I was really proud of this work. But I encourage you to read Michael T. Quick’s PhD thesis Nonlinear and Dynamic Properties of Low-Dimensional Semiconductors instead. Still, a little bit of background:
When Michael Quick, Alexander Achstein and I met, they had just realized that current theories of the charge carrier mobility (e.g. the electric current) in nanostructures as probed by THz spectroscopy are rather inadequate given their classical nature and the made approximations. Thus, a first approach was made to describe the systems quantum mechanically yet still only assuming periodic perturbations. So as part of my B.Sc. thesis, we decided that I would extend his theory to the typical Gaussian pulses as they are actually used in experiments. Yet, a long chain of problems followed and it became evident that a much more sophisticated theory had to be developed. The results were parametric master equations for the charge carrier dynamics that sparked a series of papers from this research group of which I am naturally quite proud.
Aside from the previous papers written by Michael at that point, two textbooks were incredibly useful to me. Those were
- Nonlinear Optics by Robert W. Boyd and
- Lectures on Light: Nonlinear and Quantum Optics using the Density Matrix by Stephen C. Rand.
Truly though, Michael’s thesis is the best introduction to this specific subject. Apart from that, I recommend our paper which directly built on my thesis THz Response of Charge Carriers in Nanoparticles published in Advanced Photonics Research.