Abstract The conformal bridge transformation (CBT) is reviewed in the light of PT symmetry. Originally, CBT was presented as a non-unitary (a complex canonical classical case) that relates two different forms dynamics sense Dirac. Namely, it maps a...

We propose a general analytic method to study the localization transition in one-dimensional quasicrystals with parity-time ($\mathcal{PT}$) symmetry, described by complex quasiperiodic mosaic lattice models. By applying Avila's global theory of Schr\"odinger operators, we obtain exact mobility edges and prove that edge is identical boundary $\mathcal{PT}$-symmetry breaking, which also proves e...

We examine in detail the possibilty of applying Darboux transformation to non Hermitian hamiltonians. In particular we propose a simple method of constructing exactly solvable PT symmetric potentials by applying Darboux transformation to higher states of an exactly solvable PT symmetric potential. It is shown that the resulting hamiltonian and the original one are pseudo supersymmetric partners...

Spectra of the second derivative operators corresponding to the special PT -symmetric point interactions are studied. The results are partly the completion of those obtained in [1]. The particular PT -symmetric point interactions causing unusual spectral effects are investigated for the systems defined on a finite interval as well. The spectrum of this type of interactions is very far from the ...