Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Faraday law, oxidation numbers, and ionic conductivity: The role of
  topology   Faraday's experiment measures -- within a modern view -- the charge
adiabatically transported over a macroscopic distance by a given nuclear
species in insulating liquids: the reason why it is integer is deeply rooted in
topology. Whole numbers enter chemistry in a different form: atomic oxidation
states. They are not directly measurable, and are determined instead from an
agreed set of rules. Insulating liquids are a remarkable exception: Faraday's
experiment indeed measures the oxidation numbers of each dissociated component
in the liquid phase, whose topological values are unambiguous. Ionic
conductivity in insulating liquids is expressed in terms of the autocorrelation
function of the fluctuating charge current at a given temperature in zero
electric field; topology plays a major role in this important observable as
well. The existing literature deals with the above issues by adopting the
independent-electron framework; here I provide the many-body generalization of
all the above findings, which furthermore allows for compact and very
transparent notations and formulas.

21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph