Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Embedding, simulation and consistency of $\cal PT$ -symmetric quantum
  Theory   A physical requirement on the Hamiltonian operator in quantum mechanics is
that it must generate real energy spectrum and unitary time evolution. While
the Hamiltonians are Dirac Hermitian in conventional quantum mechanics, they
observe $\cal PT$-symmetry in $\cal PT$-symmetric quantum theory. The embedding
property was first studied by G\"{u}nther and Samsonov to visualize the
evolution of unbroken $\cal PT$-symmetric Hamiltonians on $\mathbb C^2$ by
Hermitian Hamiltonians on $\mathbb C^4$. This paper investigates the properties
of $\cal PT$-symmetric quantum systems including the embedding property. We
provide a full characterization of the embedding property in the general case
and show that only unbroken $\cal PT$-symmetric quantum systems admit this
property in a finite dimensional space. Furthermore, utilizing this property,
we establish a physically realizable simulation process of the unbroken $\cal
PT$-symmetric Hamiltonians. An observation that the unbroken $\cal
PT$-symmetric quantum systems can be viewed as open systems in the conventional
quantum mechanics accounts for the consistency of $\cal PT$-symmetric quantum
theory.

10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph