Understanding Spin-Orbit Coupling in Hamiltonian

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    Coupling Spin-orbit
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Discussion Overview

The discussion revolves around the Hamiltonian of spin-orbit coupling, specifically its formulation and the interpretation of its terms. Participants explore its origins, relevance in the context of bosonic systems, and the implications of treating bosons as having pseudo spin-1/2 states.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant presents a Hamiltonian for spin-orbit coupling and requests clarification on its derivation and the significance of each term.
  • Another participant questions the source of the Hamiltonian and notes discrepancies with the version found in the referenced article.
  • A later reply expresses skepticism about the claims made in the article regarding spin-1/2 for bosons, suggesting that it may not be as general as asserted.
  • One participant acknowledges confusion about the concept of spin-1/2 for bosons but later finds that there are pseudo spin-1/2 states applicable in this context.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of the Hamiltonian or the claims made in the referenced article. There are competing views regarding the treatment of bosons and the interpretation of spin states.

Contextual Notes

There are unresolved questions regarding the derivation of the Hamiltonian and the definitions of terms used. The discussion also highlights the need for clarity on the applicability of spin-1/2 concepts to bosonic systems.

Tianyou
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Hello,
I see a Hamiltonian of spin-orbit coupling, it is like this
H=\frac{1}{2m} \sum_{\alpha} \left( \left( -\partial_{\alpha}^2 - 2i\kappa_{\alpha} \sigma_{\alpha} \partial_{\alpha} \right) + \kappa_{\alpha}^2\right)

Here \hbar = 1. \kappa_{\alpha} is the strength of spin-orbit coupling, and \sigma_{\alpha} (\alpha = x, y, z) 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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Where did you see it?
 
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.
 

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