Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal scarring for eigenfunctions of quantum graphs   We prove the existence of scarred eigenstates for star graphs with scattering
matrices at the central vertex which are either a Fourier transform matrix, or
a matrix that prohibits back-scattering. We prove the existence of scars that
are half-delocalised on a single bond. Moreover we show that the scarred states
we construct are maximal in the sense that it is impossible to have quantum
eigenfunctions with a significantly lower entropy than our examples.
  These scarred eigenstates are on graphs that exhibit generic spectral
statistics of random matrix type in the large graph limit, and, in contrast to
other constructions, correspond to non-degenerate eigenvalues; they exist for
almost all choices of lengths.

31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs