# “Classical” limit of Quantum Hall Effect

Imagine a partially filled $\nu=1$ state of the integer quantum Hall effect (IQHE). One way to think about it is to imagine a gas of electrons where each particle is locked to the lowest quantum state of their circular motion (a Gaussian wave-packet in both $x$ and $y$ with the characteristic length being the magnetic length $l_0$). When this gas becomes degenerate, we get a fully filled $v=1$ Landau level and the bulk conductivity vanishes.

I wonder, how does a single-particle theory of a partially filled$\nu=1$ IQH state state look like in terms of such particles? What is the kinetic energy term? I seek a kind of field theory for this, valid on the scales of $k \ll l_0^{-1}$ and regularized in a consistent way on the scale of $l_0$. Perhaps a tight-binding-like lattice model?

I would bet it has been done (if possible at all) by some "high-flying" quantum field theorists out there , but I have not seen such concept being used in "down-to-Earth" experiment-oriented calculations of IQHE.

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Sorry for being so vague, it's more a search of a question than than asking a well-defined answer. –  Slaviks Aug 20 '11 at 17:54

It seems I was too quick to judge and missed your point. So is the essence of you answer that a "rarified" ($\nu <1$) 2D gas is interaction-dominated? –  Slaviks Aug 21 '11 at 9:22