What Are Some Advanced Quantum Project Ideas Involving Second Quantization?

[maverick_starstrider]

Hi everyone,

In my advanced quantum course (I'm a master's student) I'm supposed to give a 40 minute talk about something that I find interesting that is related to our course material (which is basically anything in quantum. We basically covered: scattering theory, many-body stuff (second quantization) and relativistic QM (KG and dirac equations but we stopped just before QFT)) and I'm having difficulty coming up with a topic. I would really like to do something related to second quantization. Something where I could apply a second quantization approach to say quasi particles in a system and do some straightforward manipulations to get some experimentally verified predictions. Can anyone help me with topic suggestions? (NOTE: we covered BCS theory pretty explicitly so I can't do that although that's the kind of thing I'd like to do). So far I've been thinking of things like:

-Quantum Hall Effect
-Magnetic Monopoles as Excitations in a Lattice

I don't know much about these things and I was wondering if anyone could tell me if there is a semi-straightforward second quantized theory for the things that produces interesting results or could just suggest a new topic.

 

[badphysicist]

Mean-field theory of ferromagnetism and antiferromagnetism might be a good idea. It is right along the same lines as the BCS theory that you covered I am guessing. Somewhere in Gerald Mahan's Many Particle Physics book there is at least some of the derivations for this. Beware though, I have found some typos in his book including in these sections.