Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties

Details Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties

2006-10-10

arxiv.org/abs/math-ph/0610024v3

Nucl.Phys.B773:107-136,2007

Physics

Mathematical Physics

31 pp., detailed discussion of PT symmetry and more of relevant refs are added

Scientific paper

10.1016/j.nuclphysb.2007.03.016

We study complex potentials and related non-diagonalizable Hamiltonians with special emphasis on formal definitions of associated functions and Jordan cells. The nonlinear SUSY for complex potentials is considered and the theorems characterizing its structure are presented. We present the class of potentials invariant under SUSY transformations for non-diagonalizable Hamiltonians and formulate several results concerning the properties of associated functions . We comment on the applicability of these results for softly non-Hermitian PT-symmetric Hamiltonians. The role of SUSY (Darboux) transformations in increasing/decreasing of Jordancells in SUSY partner Hamiltonians is thoroughly analyzed and summarized in the Index Theorem. The properties of non-diagonalizable Hamiltonians as well as the Index Theorem are illustrated in the solvable examples of non-Hermitian reflectionless Hamiltonians . The rigorous proofs are relegated to the Part II of this paper. At last, some peculiarities in resolution of identity for discrete and continuous spectra with a zero-energy bound state at threshold are discussed.

Affiliated with

Also associated with

No associations

Rating

Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-438226