Classical Integrable 2-dim Models Inspired by SUSY Quantum Mechanics

A class of integrable 2-dim classical systems with integrals of motion of fourth order in momenta is obtained from the quantum analogues with the help of deformed SUSY algebra. With similar technique a new class of potentials connected with Lax method is found which provides the integrability of corresponding 2-dim hamiltonian systems. In addition, some integrable 2-dim systems with potentials expressed in elliptic functions are explored.Comment: 19 pages, LaTeX, final version to be published in J.Phys.

Factorization of non-linear supersymmetry in one-dimensional Quantum Mechanics. II: proofs of theorems on reducibility

In this paper, we continue to study factorization of supersymmetric (SUSY) transformations in one-dimensional Quantum Mechanics into chains of elementary Darboux transformations with nonsingular coefficients. We define the class of potentials that are invariant under the Darboux - Crum transformations and prove a number of lemmas and theorems substantiating the formulated formerly conjectures on reducibility of differential operators for spectral equivalence transformations. Analysis of the general case is performed with all the necessary proofs.Comment: 13 page

New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach

New solutions for second-order intertwining relations in two-dimensional SUSY QM are found via the repeated use of the first order supersymmetrical transformations with intermediate constant unitary rotation. Potentials obtained by this method - two-dimensional generalized P\"oschl-Teller potentials - appear to be shape-invariant. The recently proposed method of $SUSY-$separation of variables is implemented to obtain a part of their spectra, including the ground state. Explicit expressions for energy eigenvalues and corresponding normalizable eigenfunctions are given in analytic form. Intertwining relations of higher orders are discussed.Comment: 21 pages. Some typos corrected; imrovements added in Subsect.4.2; some references adde

Factorization of nonlinear supersymmetry in one-dimensional Quantum Mechanics. I: general classification of reducibility and analysis of the third-order algebra

We study possible factorizations of supersymmetric (SUSY) transformations in the one-dimensional quantum mechanics into chains of elementary Darboux transformations with nonsingular coefficients. A classification of irreducible (almost) isospectral transformations and of related SUSY algebras is presented. The detailed analysis of SUSY algebras and isospectral operators is performed for the third-order case.Comment: 16 page

Matching meson resonances to OPE in QCD

We investigate the possible corrections to the linear Regge trajectories for the light-quark meson sector by matching two-point correlators of quark currents to the Operator Product Expansion. We find that the allowed modifications to the linear behavior must decrease rapidly with the principal quantum number. After fitting the lightest states in each channel and certain low-energy constants the whole spectrum for meson masses and residues is obtained in a satisfactory agreement with phenomenology. The perturbative corrections to our results are discussed.Comment: 4 pages, talk given at the First Workshop on Quark Hadron Duality and the Transition to pQCD (June 2005, Frascati, Italy) and at the International Conference on QCD and Hadronic Physics (June 2005, Beijing, China

Higher Order Matrix SUSY Transformations in Two-Dimensional Quantum Mechanics

The iteration procedure of supersymmetric transformations for the two-dimensional Schroedinger operator is implemented by means of the matrix form of factorization in terms of matrix 2x2 supercharges. Two different types of iterations are investigated in detail. The particular case of diagonal initial Hamiltonian is considered, and the existence of solutions is demonstrated. Explicit examples illustrate the construction.Comment: 15