Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantisations of piecewise affine maps on the torus and their quantum
  limits   For general quantum systems the semiclassical behaviour of eigenfunctions in
relation to the ergodic properties of the underlying classical system is quite
difficult to understand. The Wignerfunctions of eigenstates converge weakly to
invariant measures of the classical system, the so called quantum limits, and
one would like to understand which invariant measures can occur that way,
thereby classifying the semiclassical behaviour of eigenfunctions. We introduce
a class of maps on the torus for whose quantisations we can understand the set
of quantum limits in great detail. In particular we can construct examples of
ergodic maps which have singular ergodic measures as quantum limits, and
examples of non-ergodic maps where arbitrary convex combinations of absolutely
continuous ergodic measures can occur as quantum limits. The maps we quantise
are obtained by cutting and stacking.

7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs