Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonadiabatic transitions in Landau-Zener grids: integrability and
  semiclassical theory   We demonstrate that the general model of a linearly time-dependent crossing
of two energy bands is integrable. Namely, the Hamiltonian of this model has a
quadratically time-dependent commuting operator. We apply this property to
four-state Landau-Zener (LZ) models that have previously been used to describe
the Landau-St\"uckelberg interferometry experiments with an electron shuttling
between two semiconductor quantum dots. The integrability then leads to simple
but nontrivial exact relations for the transition probabilities. In addition,
the integrability leads to a semiclassical theory that provides analytical
approximation for the transition probabilities in these models for all
parameter values. The results predict a dynamic phase transition, and show that
similarly-looking models belong to different topological classes.

1
The categories of this paper are: cs
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci