Justify the connection between the quantum and classical hall effect slightly be...

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justify this slightly better

milestones:

https://github.com/ThomasFKJorna/thesis-writing/blob/5f1acf2c13d516eabf341771a257f2f66d67c8a1/Chapters/III. Anyons/4. The Quantum Hall Effect (conflicted).md#L34

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  - subchapter
Title: 4. The Quantum Hall Effect (conflicted)
Ctime: 20220517090956
Mtime: 20220517115532
---

# 4. The Quantum Hall Effect (conflicted)

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- Following @Norton2012, we know how to interpret this: we can demote an idealization to an approximation if we are able to show that there is a
    smooth limit.
- This is exactly the problem, according to @shech2019 the topological explanation of anyons requires an _exact_ 2d system (or a rather ad-hoc 2d system as we saw).
- Therefore we cannot call this approximately 2d.
- According to @shech2019, this is a problem for those with nominalist inclinations,[^1] as the instantiation of abstract mathematical structures in the real world would be an issue.
- Such an argument can only be made, however, through the use of the eia which was discussed in the previous (or next?) chapter.
- Therefore, it would do such people well to examine the physical effect thoroughly for any signs of this.

In this chapter, we will examine the inner working of the Quantum Hall Effect. This is needed in order to understand the following

1) why do people say that these particles are anyons
2) what idealizations are made in the explanation of the Quantum Hall Effect separate from the topological one.
3) to calculate the berry phase

Readers less interested in the details can skip to the last subsection of this section `link` and the next section `link`.

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The Quantum Hall Effect is the quantum version of the classical hall effect, a rather straightforward consequence of moving charged particles in a magnetic field. It was discovered all the way back in `xxxx` by edwin hall, who claimed it a novelty which would never have any use-case.

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Today hall-effect sensors are widely used to pick up magnetic fields and rotations of conducting materials. More esoteric applications are as potential long-term space-travel propellants in so-called hall-effect thrusters, which are a specific form of ion propolsion, which can generate a low thrust for a very long amount of time.

{/** TODO: Rewrite the basics of the Classical Hall Effect in words, not bullet points
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The basics of the effect are rather simple

- strip which has current flowing through it.
- magnetic field perpendicular to that strip