Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: dc conductivity as a geometric phase   The zero frequency conductivity ($D_c$), the criterion to distinguish between
conductors and insulators is expressed in terms of a geometric phase. $D_c$ is
also expressed using the formalism of the modern theory of polarization. The
tenet of Kohn [{\it Phys. Rev.} {\bf 133} A171 (1964)], namely, that insulation
is due to localization in the many-body space, is refined as follows.
Wavefunctions which are eigenfunctions of the total current operator give rise
to a finite $D_c$ and are therefore metallic. They are also delocalized.
Several examples which corroborate the results are presented, as well as a
numerical implementation. The formalism is also applied to the Hall
conductance, and the quantization condition for zero Hall conductance is
derived to be $\frac{e\Phi_B}{N h c} = \frac{Q}{M}$, with $Q$ and $M$ integers.

9
The categories of this paper are: nlin
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
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The categories of this paper are: adap-org