3 research outputs found
SUSY transformations with complex factorization constants. Application to spectral singularities
Supersymmetric (SUSY) transformation operators corresponding to complex
factorization constants are analyzed as operators acting in the Hilbert space
of functions square integrable on the positive semiaxis. Obtained results are
applied to Hamiltonians possessing spectral singularities which are
non-Hermitian SUSY partners of selfadjoint operators. A new regularization
procedure for the resolution of the identity operator in terms of continuous
biorthonormal set of the non-Hermitian Hamiltonian eigenfunctions is proposed.
It is also shown that the continuous spectrum eigenfunction has zero binorm (in
the sense of distributions) at the singular point.Comment: Thanks to A. Sokolov a number of inaccuracies are correcte
Spectral singularities and Bragg scattering in complex crystals
Spectral singularities that spoil the completeness of Bloch-Floquet states
may occur in non-Hermitian Hamiltonians with complex periodic potentials. Here
an equivalence is established between spectral singularities in complex
crystals and secularities that arise in Bragg diffraction patterns. Signatures
of spectral singularities in a scattering process with wave packets are
elucidated for a PT-symmetric complex crystal.Comment: 6 pages, 5 figures, to be published in Phys. Rev.