Non-hermitian Hamiltonians with unitary and antiunitary symmetries

FRANCISCO M. FERNÁNDEZ; JAVIER GARCIA

ANNALS OF PHYSICS (NEW YORK)

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2014 vol. 342 p. 195 - 204

0003-4916

We analyse 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 analyse their properties separately. One of the main results of this paper is that some PT-symmetric Hamiltonians with point-group symmetry C2v 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-groupsymmetry enables us to explain such anomalous behaviour and to choose a suitable antiunitary operator for the PT symmetry.