August 2013
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Day August 29, 2013

PT-symmetry broken by point-group symmetry

Francisco M Fernández, Javier Garcia

We discuss a PT-symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schrodinger equation for a particle in a square box with the PT-symmetric potential \(V(x,y)=iaxy\). Perturbation theory clearly shows that some of the eigenvalues are complex for sufficiently small values of \(|a|\). Point-group symmetry proves useful to guess if some of the eigenvalues may already be complex for all values of the coupling constant. We confirm those conclusions by means of an accurate numerical calculation based on the diagonalization method. On the other hand, the Schrodinger equation with the potential \(V(x,y)=iaxy^{2}\) exhibits real eigenvalues for sufficiently small values of \(|a|\). Point group symmetry suggests that PT-symmetry may be broken in the former case and unbroken in the latter one.
Quantum Physics (quant-ph)