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Spin-orbit coupling

by Tianyou
Tags: coupling, spinorbit
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Tianyou
#1
Apr10-14, 10:23 PM
P: 4
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.
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DrDu
#2
Apr11-14, 10:34 AM
Sci Advisor
P: 3,547
Where did you see it?
Tianyou
#3
Apr13-14, 09:52 PM
P: 4
I saw this hamiltonian in an article in arXiv titled "Enhancement of condensate depletion due to spin-orbit coupling".

DrDu
#4
Apr14-14, 01:44 AM
Sci Advisor
P: 3,547
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.
Tianyou
#5
Apr14-14, 09:13 PM
P: 4
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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