Category Universite de Bourgogne

Quadratic PT-symmetric operators with real spectrum and similarity to self-adjoint operators

Emanuela Caliceti, Sandro Graffi, Michael Hitrik, Johannes Sjoestrand

It is established that a PT-symmetric elliptic quadratic differential operator with real spectrum is similar to a self-adjoint operator precisely when the associated fundamental matrix has no Jordan blocks.
Mathematical Physics (math-ph); Quantum Physics (quant-ph)

PT symmetry and Weyl asymptotics

Johannes Sjoestrand

For a class of PT-symmetric operators with small random perturbations, the eigenvalues obey Weyl asymptotics with probability close to 1. Consequently, when the principal symbol is non-real, there are many non-real eigenvalues.
Spectral Theory (math.SP)