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A Vortex triangular lattice

  1. Sep 4, 2016 #1
    Hello everyone,
    I am not an expert in the topic so I apologize in advance if the question has an easy answer. I think it is well known that if we have a set of N vortices in a superfluid their mutual interaction is logarithmic. Meaning that if [itex]\vec x_n[/itex] is the position of the n-th vortex, then the potential between them is of the form

    $$
    V(\{\vec x_n\})\propto-\sum_{n=1}^N\sum_{m<n}\log|\vec x_n-\vec x_m|
    $$

    I also know that the vortices will arrange themselves on a triangular lattice.

    Does anyone know how to show that starting from the previous potential?

    Thanks!
     
  2. jcsd
  3. Sep 8, 2016 #2

    DrClaude

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    Staff: Mentor

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