Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-linear Supersymmetry for non-Hermitian, non-diagonalizable
  Hamiltonians: I. General properties   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.

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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex