Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-hermitean hamiltonians with unitary and antiunitary symmetry   We analyze several non-Hermitian Hamiltonians with antiunitary symmetry from
the point of view of their point-group symmetry. It enables us to predict the
degeneracy of the energy levels and to reduce the dimension of the matrices
necessary for the diagonalization of the Hamiltonian in a given basis set. We
can also classify the solutions according to the irreducible representations of
the point group and thus analyze their properties separately. One of the main
results of this paper is that some PT-symmetric Hamiltonians with point-group
symmetry $C_{2v}$ exhibit complex eigenvalues for all values of a potential
parameter. In such cases the PT phase transition takes place at the trivial
Hermitian limit which suggests that the phenomenon is not robust. Point-group
symmetry enables us to explain such anomalous behaviour and to choose a
suitable antiunitary operator for the PT symmetry.

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The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas