Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Link between Integrability, Level Crossings, and Exact Solution in
  Quantum Models   We investigate the connection between energy level crossings in integrable
systems and their integrability, i.e. the existence of a set of non-trivial
integrals of motion. In particular, we consider a general quantum Hamiltonian
linear in the coupling u, H(u) = T + uV, and require that it has the maximum
possible number of nontrivial commuting partners also linear in u. We
demonstrate how this commutation requirement alone leads to: (1) an exact
solution for the energy spectrum and (2) level crossings, which are always
present in these Hamiltonians in violation of the Wigner-von Neumann
non-crossing rule. Moreover, we construct these Hamiltonians explicitly by
resolving the above commutation requirement and show their equivalence to a
sector of Gaudin magnets (central spin Hamiltonians). In contrast, fewer than
the maximum number of conservation laws does not guarantee level crossings.

23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph