Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The stochastic limit of the Fr\"ohlich Hamiltonian: relations with the
  quantum Hall effect   We propose a model of an approximatively two--dimensional electron gas in a
uniform electric and magnetic field and interacting with a positive background
through the Fr\"ohlich Hamiltonian. We consider the stochastic limit of this
model and we find the quantum Langevin equation and the generator of the master
equation. This allows us to calculate the explicit form of the conductivity and
the resistivity tensors and to deduce a {\it fine tuning condition} (FTC)
between the electric and the magnetic fields. This condition shows that the
$x$--component of the current is zero unless a certain quotient, involving the
physical parameters, takes values in a finite set of physically meaningful
rational numbers. We argue that this behaviour is quite similar to that
observed in the quantum Hall effect. We also show that, under some conditions
on the form factors entering in the definition of the model, also the plateaux
and the "almost" linear behaviour of the Hall resistivity can be recovered. Our
FTC does not distinguish between fractional and integer values.

25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph