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Spin-orbit coupling

  1. Apr 10, 2014 #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. Apr 11, 2014 #2

    DrDu

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    Where did you see it?
     
  4. Apr 13, 2014 #3
    I saw this hamiltonian in an article in arXiv titled "Enhancement of condensate depletion due to spin-orbit coupling".
     
  5. Apr 14, 2014 #4

    DrDu

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    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. Apr 14, 2014 #5
    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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