August 2012
Mon Tue Wed Thu Fri Sat Sun
« Jul   Sep »
12345
6789101112
13141516171819
20212223242526
2728293031

## On the metric operator for the imaginary cubic oscillator

Petr Siegl, David Krejcirik

We show that the eigenvectors of the PT -symmetric imaginary cubic oscillator are complete, but do not form a Riesz basis. This results in the existence of a bounded metric operator having intrinsic singularity reflected in the inevitable unboundedness of the inverse. Moreover, the existence of nontrivial pseudospectrum is observed. In other words, there is no quantum-mechanical Hamiltonian associated with it via bounded and boundedly invertible similarity transformations. These results open new directions in physical interpretation of PT -symmetric models with intrinsically singular metric, since their properties are essentially different with respect to self-adjoint Hamiltonians, for instance, due to spectral instabilities.

http://arxiv.org/abs/1208.1866
Quantum Physics (quant-ph); Mathematical Physics (math-ph)
Physical Review D 86, 121702 (2012)