A globally diagonalizable alpha^2-dynamo operator, SUSY QM and the Dirac equation

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) transfo…

Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: II. Rigorous results

We continue our investigation of the nonlinear SUSY for complex potentials started in the Part I (math-ph/0610024) and prove the theorems characterizing its structure in the case of non-diagonalizable Hamiltonians. This part provides the mathematical basis of previous studies. The classes of potentials invariant under SUSY transformations for non-diagonalizable Hamiltonians are specified and the asymptotics of formal eigenfunctions and associated functions are derived. Several results on the normalizability of associated functions at infinities are rigorously proved. Finally the Index Theorem …

来自杨-巴克斯特方程常数非可逆解的非厄米可积系统

Non-hermitian integrable systems from constant non-invertible solutions of the Yang-Baxter equation

本文利用超对称代数对常数非可逆杨-巴克斯特解进行巴克斯特化，构造出可逆$R$-矩阵，进而得到非厄米可积自旋链哈密顿量，并发现两个新模型。