Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localization in infinite billiards: a comparison between quantum and
  classical ergodicity   Consider the non-compact billiard in the first quandrant bounded by the
positive $x$-semiaxis, the positive $y$-semiaxis and the graph of $f(x) =
(x+1)^{-\alpha}$, $\alpha \in (1,2]$. Although the Schnirelman Theorem holds,
the quantum average of the position $x$ is finite on any eigenstate, while
classical ergodicity entails that the classical time average of $x$ is
unbounded.

8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th