Thermodynamics of a Spinor Bose Gas

This is the project that I undertook for my honors thesis (2006). The idea was to investigate the thermodynamics and fractional exclusion statistics of a gas that was confined to a single dimension. In particular, we looked at a gas of particles with spin half obeying boson statistics. While this sounds a bit weird, by considering bosonic gases in the ground state and the first excited state (a hyperfine excitation), you can have a pseudo-spin half system. The reason for looking at this system was because optics experiments were beginning to confine atoms to long, thin cigar shaped traps using optical lattices, in which the particles essentially behaved as confined to a one-dimensional potential. However, what got me interested in this project was the question "How does the spin half degree of freedom change things from a gas of bosons?" Alas, I don't think I ever answered that question to my satisfaction.

I ended up finding results that contradicted previous work, and I didn't have time to delve to the bottom of that issue. There are two important parameters in the system that I was interested in, namely the temperature T and the coupling strength, which I called c. I now think I took the limit as T approached zero while maintaining the product cT in order to obtain the low temperature behavior, which led to different results than I expected. I wasn't quite developed enough in my physical intuition at the time to realise this, however.

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