Hello, I see a Hamiltonian of spin-orbit coupling, it is like this H=[itex]\frac{1}{2m} \sum_{\alpha} \left( \left( -\partial_{\alpha}^2 - 2i\kappa_{\alpha} \sigma_{\alpha} \partial_{\alpha} \right) + \kappa_{\alpha}^2\right)[/itex] Here [itex]\hbar = 1. \kappa_{\alpha} [/itex] is the strength of spin-orbit coupling, and [itex] \sigma_{\alpha} (\alpha = x, y, z)[/itex] are Pauli matrices. Can someone explain to me where this hamiltonian comes from? What is the meaning of each term? Thank you.
I saw this hamiltonian in an article in arXiv titled "Enhancement of condensate depletion due to spin-orbit coupling".
Next time, it would be kind of you to give either a link or at least a full reference for an article. The hamiltonian in that article does not coincide completely with the one of your first post. However, I don't know where it comes from. Did you check the articles they are citing? To me, it looks rather dubious. Spin 1/2 for bosons? Certainly not as general as they claim it to be.
I am confused for the Spin 1/2 for the bosons before. I checked it and found that in this system there is a pseudo Spin 1/2 states for the bosons.