Spin-orbit coupling

  1. 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.
  2. jcsd
  3. DrDu

    DrDu 4,636
    Science Advisor

    Where did you see it?
  4. I saw this hamiltonian in an article in arXiv titled "Enhancement of condensate depletion due to spin-orbit coupling".
  5. DrDu

    DrDu 4,636
    Science Advisor

    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.
  6. 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.
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