# Can the Vortices in a Superfluid Form a Triangular Lattice?

• A
• Einj
In summary, the conversation discusses the interaction between a set of N vortices in a superfluid, which is known to be logarithmic. The potential between the vortices is expressed as a sum of logarithmic terms, and it is also mentioned that the vortices arrange themselves on a triangular lattice. The question asks for a method to show this potential starting from the previous one. A possible resource for this is suggested as V. K. Tkachenko's article in the Soviet Phys. JETP.
Einj
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 $\vec x_n$ 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!

## 1. What is a vortex triangular lattice?

A vortex triangular lattice is a pattern produced by vortices, which are swirling regions of fluid flow, arranged in a triangular shape. This lattice structure is often observed in superconductors and superfluids.

## 2. How is a vortex triangular lattice formed?

A vortex triangular lattice is formed when vortices are pinned in place by defects or impurities in the material. This results in a regular arrangement of vortices, forming a triangular lattice pattern.

## 3. What are the properties of a vortex triangular lattice?

A vortex triangular lattice has unique properties, such as a high degree of symmetry, that make it useful for studying the behavior of superconductors and superfluids. It also has a strong resistance to external forces, making it difficult to disrupt the lattice structure.

## 4. What applications does a vortex triangular lattice have?

Vortex triangular lattices have potential applications in areas such as quantum computing, data storage, and energy harvesting. They can also be used to study the properties of superconductors and superfluids, which have various practical applications in technology.

## 5. How does temperature affect a vortex triangular lattice?

The formation and behavior of a vortex triangular lattice is highly dependent on temperature. As the temperature increases, the strength of the lattice structure decreases, making it easier to disrupt. At very low temperatures, the vortices may arrange themselves in a more complex pattern, such as a square or hexagonal lattice.

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