Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semiclassical measures for higher dimensional quantum cat maps   Consider a quantum cat map $M$ associated to a matrix
$A\in\mathop{\mathrm{Sp}}(2n,\mathbb Z)$, which is a common toy model in
quantum chaos. We show that the mass of eigenfunctions of $M$ on any nonempty
open set in the position-frequency space satisfies a lower bound which is
uniform in the semiclassical limit, under two assumptions: (1) there is a
unique simple eigenvalue of $A$ of largest absolute value and (2) the
characteristic polynomial of $A$ is irreducible over the rationals. This is
similar to previous work [arXiv:1705.05019], [arXiv:1906.08923] on negatively
curved surfaces and [arXiv:2103.06633] on quantum cat maps with $n=1$, but this
paper gives the first results of this type which apply in any dimension. When
condition (2) fails we provide a weaker version of the result and discuss
relations to existing counterexamples. We also obtain corresponding statements
regarding semiclassical measures and damped quantum cat maps.

37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga