Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Algorithmic Integrability: The Metaphor of Polygonal Billiards   An elementary application of Algorithmic Complexity Theory to the polygonal
approximations of curved billiards-integrable and chaotic-unveils the
equivalence of this problem to the procedure of quantization of classical
systems: the scaling relations for the average complexity of symbolic
trajectories are formally the same as those governing the semi-classical limit
of quantum systems. Two cases-the circle, and the stadium-are examined in
detail, and are presented as paradigms.

20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con